solidi current topics in solid state physics The role of breathers in the anomalous decay of luminescence
|
|
- Kristian Benson
- 5 years ago
- Views:
Transcription
1 solidi status physia pss urrent topis in solid state physis The role of breathers in the anomalous deay of luminesene Eva Miho kova and Lawrene S. Shulman Institute of Physis, ASCR, Cukrovarnika, Prague 6, 6 53, Czeh Republi Physis Department, Clarkson University, Potsdam, NY, , USA Reeived 7 June 6, revised July 6, aepted July 6 Published online November 6 PACS 5.45.Yv, 3.7.Hq, 63..Ry, m Luminesene of alkali halides doped by heavy ns ions exhibits an anomaly in the slow omponent emission deay. The anomaly is explained by the formation of a disrete breather in the immediate neighborhood of the impurity. We study properties of these breathers, their phase spae struture, robustness, and propensity for formation. Under a wide range of parameters and interioni potentials they form -dimensional Kolmogorov-Arnold-Moser tori (less than generi) in phase spae. We show strobed views of these tori, useful in quantization. All features support the thesis of breather formation as the explanation for the luminesene deay anomaly that first motivated our breather proposal. phys. stat. sol. () 3, No., (6) / DOI./pss.674 T N I R P E R
2 phys. stat. sol. () 3, No., (6) / DOI./pss.674 The role of breathers in the anomalous deay of luminesene Eva Mihóková and Lawrene S. Shulman Institute of Physis, ASCR, Cukrovarnika, Prague 6, 6 53, Czeh Republi Physis Department, Clarkson University, Potsdam, NY, , USA Reeived 7 June 6, revised July 6, aepted July 6 Published online November 6 PACS 5.45.Yv, 3.7.Hq, 63..Ry, m Luminesene of alkali halides doped by heavy ns ions exhibits an anomaly in the slow omponent emission deay. The anomaly is explained by the formation of a disrete breather in the immediate neighborhood of the impurity. We study properties of these breathers, their phase spae struture, robustness, and propensity for formation. Under a wide range of parameters and interioni potentials they form -dimensional Kolmogorov-Arnold-Moser tori (less than generi) in phase spae. We show strobed views of these tori, useful in quantization. All features support the thesis of breather formation as the explanation for the luminesene deay anomaly that first motivated our breather proposal. 6 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Introdution Breathers are spatially loalized, time-periodi, stable exitations in periodi nonlinear latties. They are known to exist in a number of systems, suh as Josephson juntions, optial waveguide arrays and laser-indued photoni rystals (see, e.g., [] and Refs. therein). In a series of studies in doped alkali halides [ 5] the following anomaly was found: rapid and non-exponential deay of luminesene during what should have been the early stages of the deay of a metastable level. This anomaly was explained by postulating extremely long rystal relaxation times. The extreme slowdown in turn was attributed to the formation of breathers in a lattie that is highly distorted by the Jahn-Teller (JT) effet [6]. The onnetion was established by simulating the dynamis of a hain of atoms along the JT axis using a quarti polynomial interatomi potential. In this paper we examine the effets of using different interatomi potentials as well as different atomi speies (in partiular different mass ratios for diatomi hains). We onfine attention to the zero-temperature ase. An interesting result is that, at least for the parameter values we study, the phase spae lassial motion of the atoms lives on a two-dimensional Kolmogorov-Arnold- Moser (KAM) torus. That is, beyond the already partiular property of regular, torus-onfined motion, that torus only has two signifiantly nonzero radii, i.e., nonzero ation variables. These results support, both physially and mathematially, the onlusions of [6]. The model and the breather in various interatomi potentials Optial properties of isolated Tl or Pb enters in alkali halide rystals an be desribed by onsidering the impurity and its six nearest neighbors (in the f lattie) to be a quasimoleule. When exited, the moleule distorts aording to the Jahn-Teller (JT) effet and its lowest exited level (whih was degenerate) is split into a radiative state, displaying exponential nanoseond deay and a metastable state, with a milliseond time sale. The latter is the state for whih the anomaly is observed. The initial deay is faster than exponential, settling into exponential deay only after a time interval on the order of milliseonds. To explain the anomaly we proposed that the lattie takes a long time to yield to the strain, thereby introduing a oupling between the two lowest exited states of the emission enter. This assumption allowed suessful fitting of low Corresponding author: mihokova@fzu.z, Phone: , Fax: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
3 phys. stat. sol. () 3, No. (6) 347 b.8.4 log Intensity Frequeny Fig. Quarti polynomial interatomi potential. a) Kineti energy of the system as a funtion of time and atom number. The inset shows the positions of the atoms vs. time. b) Fourier transforms (intensity) of the funtions (Q (t),q (t),q (t),q (t)) in urves through 4. The urves orresponding to suessive atoms are vertially shifted (downward by 4) for better display. The superimposed horizontal lines indiate where the phonon frequeny bands are. Arrows point to the prinipal frequenies of the spetrum outside the phonon bands. All other intense frequenies are resonanes or beat frequenies of these two. () The KAM torus, projeted on a plane within the four dimensional spae {Q,P,q,p }. Eah figure ontains points, with points taken per system time unit. The absissa is position and the ordinate is momentum. Loops in the torus represent projetions on the Q -P and q -p planes of the strobosopially viewed KAM torus, substantiating the assertion that the torus is two-dimensional (only has two signifiant nonzero radii). The parameters used in the simulation are N =, q =, r =, ν =4, and λ =. temperature KBr:Pb data [3], provided that the ultimate relaxation of the lattie is on the same time sale as that of the slow emission deay (ms). The model was extended to the entire olletion of Pb and Tldoped alkali halides both at liquid He temperature [4] and at higher temperatures [5]. Through modeling the dynamis of the lattie [6] we found that under lassial dynamis the energy of the extended quasi-moleule was onfined to a small neighborhood of the impurity-exitation-induedperturbation, a perturbation signifiant enough to make non-linear effets important. This onfinement led to the slowdown in relaxation needed to aount for the experimental data. We assume that the lattie anion immediately next to the impurity and along the axis of deformation is under tremendous pressure to move away from the impurity. We further assume that in studying the effet of this fore we an onfine attention to the line of atoms on this axis, effetively a hain, with the influene of the rest of the rystal expressed through a holding fore. We introdue this substrate-defining fore through a potential felt by eah ion on the hain; it defines the equilibrium position of the ion in the rystal in the absene of the speifi pressure from the displaed first anion. Note that the non-isotropi stresses imply lesser deformation for off-axis atoms. We assume an interioni potential V (u) with u the displaement ( from the ion s equilibrium position. For the simulations reported in [6] we used V (u) =Mω u + λu 4) /. The Hamiltonian is H = N n= { } P n M + rp n M + V (q n Q n )+V(Q n q n )+ν[v(q n )+V(q n )]. () Q, P are the oordinate and momentum of the anion to the right of the impurity, followed by q, p (ation), Q, P et. The Q-partiles have mass M, the q s, M/r ( r is a mass ratio). The holding fore arises from the potentials multiplying ν, so that ν an be interpreted as an effetive number of neighbors. This Hamiltonian inludes the effet of the highly distorted impurity wave funtion through the non-dynami variable q. By setting this to speifi positive values we an provide a push on the entire hain, induing intense osillation, possible breather formation, and possible wave propagation, depending on the model parameters. The system was solved numerially for the indiated potential, using units suh that M =and ω =. We found that for ertain parameters the energy deposited in the hain by the non-zero q (JT deformation) 6 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
4 348 E. Mihóková and L. S. Shuman: The role of breathers in the anomalous deay of luminesene b logintensity Frequeny Fig. Born-Mayer-Coulomb (BMC) potential: a), b), and ) as in Fig.. Parameters used in the simulation: N =, q =, r =, ν = 4. BMC parameters: αm q /d =, ρ =.3, and d = 3.3, in the notation of [7]. does not propagate but beomes bound in vibrations of the first atoms of the hain, i.e., the breather. This is illustrated in Fig. a displaying kineti energy as a funtion of time and atom number as well as the time dependene of the atomi position oordinate (in the inset). The frequeny spetrum of the first four atoms, obtained by Fast Fourier Transform (FFT) of Q (t), q (t), Q (t) q (t), is displayed in Fig. b. The spetrum shows two dominant frequenies falling above the optial phonon band and in its gap (marked by a sequene of horizontal lines). These frequenies haraterize the osillations of the breather. In Fig. we show a projetion of the KAM torus whih is the lassial phase spae orbit of the breather. Superimposed is a pair of loops, whih result from a strobosopi image of the torus [8]. The fat that these are well determined, one-dimensional loops implies that the KAM torus for our simulations is only a two dimensional struture. This is of ourse onsistent with the presene of only two dominant frequenies outside the phonon bands in the frequeny spetrum although there is no requirement that only two frequenies appear. There are many potentials used for the desription of interatomi fores. Those most frequently used are listed in [7]. Our onern was to study whether the breather is robust with respet to the hoie of interatomi potential. We alulated the hain dynamis for polynomial potential with a ubi term added, for Morse and for Born-Mayer-Coulomb potentials. All of them are softer than the originally used quarti polynomial potential. However, in all ases studied the formation of the breather was onfirmed. For illustration, the results for the Born-Mayer-Coulomb potential are shown in Fig.. 3 Preditions of the model in variety of substanes The deay anomaly has been observed in a variety of doped alkali halides. For potassium halides doped either with Tl+ or Pb+ the anomaly grows with inreasing size and mass of the lattie anion (a large anomaly is manifest for about 5 ms and enhanes deay by or 3 orders of magnitude). This ours in the sequene of latties KCl KBr KI. For the KCl lattie the anomaly, i.e. deviation from the exponential, is small (Tl+ ) or nonexistent (Pb+ ); for KBr the nonexponential part is steeper and survives to longer times for the KI survives even longer. Experimental results with Pb+ -doped alkali bromide rystals show that similar behavior is observed in the sequene of latties RbBr KBr NaBr where the lattie ation is suessively made smaller and lighter. Namely, for the RbBr rystal a weak anomaly is observed while there is a signifiant anomaly for Pb-doped KBr and NaBr rystals. To summarize, a quantity that ertainly affets the harater of the deay anomaly is, r, the ratio of the mass of the lattie anion to that of the lattie ation. In the sequene of potassium halides (KCl KBr KI) the orresponding mass ratio hanges as r to r to r 3.3. In the sequene of alkali bromides (RbBr KBr NaBr) the mass ratio goes from r to r to r 4. From the experimental point of view a very slight anomaly is observed or none at all for mass ratios lose to, while for ratios of or more the anomaly is large. How is this observation onsistent with our breather model? 6 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
5 phys. stat. sol. () 3, No. (6) 349 Kineti energy weighted position r (mass ratio) Fig. 3 Kineti energy-weighted position (in atomi spaing units) as a funtion of anion-ation mass ratio. For details see the text. The parameters used in the simulation are N =, q =.5, ν =4, and λ =.5. To study this we used our standard quarti polynomial potential. We performed lattie-dynamis simulations hanging the atomi mass ratio entering the hain model. It turns that different mass ratios an be more favorable or less favorable for forming the breather. The simulations were made for a hain of 4 atoms. As a measure of how good the breather is, whih is to say, how good is the onfinement of the energy to the region of the impurity, we alulated a kineti energy-weighted position. That is, let k be the atom number, k =for the immediate neighbor of the impurity, and ounting outward. Let w KE (k) be the average kineti energy of the k th atom. Then k KE k = k kw KE(k) k w KE(k). () The smaller this quantity is, the more the energy is onentrated in the breather, and therefore the bigger the expeted deay anomaly. The result of a systemati study of k KE as a funtion of r is shown in Fig. 3. A mass ratio higher than is favorable for forming a breather and most of the kineti energy is trapped in first atoms of the hain. For mass ratios near one most of kineti energy travels away. This is ompletely and satisfyingly onsistent with the experimental observations. 4 Conlusion For doped alkali halides, the existene of breather modes provides an answer to the puzzling anomaly observed in slow omponent emission deay. First we found that breathers formed when the interatomi potential was quarti. In the present paper breather formation has been demonstrated for other forms of interatomi potential. Thus we onlude that breather formation is a robust feature. A ompelling demonstration of breather formation is the mapping of the KAM torus. We used a strobosopi method of viewing this torus whih allowed the further observation that there were only two nonzero radii (or ation variables) for the torus. Systemati physial observations suggest that alkali halides for whih the anion-ation mass ratio is lose to one have little or no anomaly in their luminesene deay. We found here that breather formation exhibits a similar effet: as this ratio approahes unity the breather gets more and more deloalized, and for appropriate parameters disappears ompletely. Aknowledgements The support of the projet KONTAKT MSMT P5ME73 and of NSF grant are gratefully aknowledged. Referenes [] V. Fleurov, Chaos 3, 676 (3). [] K. Polák, M. Nikl, and E. Mihóková, J. Lumin. 54, 89 (99). [3] B. Gaveau et al., Phys. Rev. B 58, 6938 (998). [4] B. Gaveau et al., J. Lumin. 9, 3 (). [5] E. Mihóková et al., Phys. Rev. B 66, 55 (). [6] L. S. Shulman et al., Phys. Rev. Lett. 88, 4 (). [7] S. A. Kiselev et al., Phys. Rev. B 5, 935 (994). [8] L. S. Shulman, Phys. Rev. A 68, 59 (3). 6 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
The gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationpss A multi-sensor study of Cl 2 etching of polycrystalline Si solidi status physica Pete I. Klimecky and Fred L. Terry, Jr. *
phys. stat. sol. () 5, No. 5, 5 (8) / DOI./pss.77787 A multi-sensor study of Cl ething of polyrystalline Si physia pss www.pss-.om urrent topis in solid state physis Pete I. Klimeky and Fred L. Terry,
More informationEvaluation of effect of blade internal modes on sensitivity of Advanced LIGO
Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple
More informationELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES.
ELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES. All systems with interation of some type have normal modes. One may desribe them as solutions in absene of soures; they are exitations of the system
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationRESEARCH ON RANDOM FOURIER WAVE-NUMBER SPECTRUM OF FLUCTUATING WIND SPEED
The Seventh Asia-Paifi Conferene on Wind Engineering, November 8-1, 9, Taipei, Taiwan RESEARCH ON RANDOM FORIER WAVE-NMBER SPECTRM OF FLCTATING WIND SPEED Qi Yan 1, Jie Li 1 Ph D. andidate, Department
More informationEnergy Gaps in a Spacetime Crystal
Energy Gaps in a Spaetime Crystal L.P. Horwitz a,b, and E.Z. Engelberg a Shool of Physis, Tel Aviv University, Ramat Aviv 69978, Israel b Department of Physis, Ariel University Center of Samaria, Ariel
More informationphysica status solidi current topics in solid state physics
physia pss urrent topis in solid state physis Eletromagnetially indued transpareny in asymmetri double quantum wells in the transient regime Leonardo Silvestri1 and Gerard Czajkowski2 1 2 Dipartimento
More informationIntroduction to Quantum Chemistry
Chem. 140B Dr. J.A. Mak Introdution to Quantum Chemistry Without Quantum Mehanis, how would you explain: Periodi trends in properties of the elements Struture of ompounds e.g. Tetrahedral arbon in ethane,
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationApplication of the Dyson-type boson mapping for low-lying electron excited states in molecules
Prog. Theor. Exp. Phys. 05, 063I0 ( pages DOI: 0.093/ptep/ptv068 Appliation of the Dyson-type boson mapping for low-lying eletron exited states in moleules adao Ohkido, and Makoto Takahashi Teaher-training
More informationPhysics 486. Classical Newton s laws Motion of bodies described in terms of initial conditions by specifying x(t), v(t).
Physis 486 Tony M. Liss Leture 1 Why quantum mehanis? Quantum vs. lassial mehanis: Classial Newton s laws Motion of bodies desribed in terms of initial onditions by speifying x(t), v(t). Hugely suessful
More informationWhere as discussed previously we interpret solutions to this partial differential equation in the weak sense: b
Consider the pure initial value problem for a homogeneous system of onservation laws with no soure terms in one spae dimension: Where as disussed previously we interpret solutions to this partial differential
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 6 (2/24/04) Energy Transfer Kernel F(E E')
22.54 Neutron Interations and Appliations (Spring 2004) Chapter 6 (2/24/04) Energy Transfer Kernel F(E E') Referenes -- J. R. Lamarsh, Introdution to Nulear Reator Theory (Addison-Wesley, Reading, 1966),
More informationFour-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field
Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia
More informationStability Analysis of Orbital Motions around Uniformly Rotating Irregular Asteroids
Stability Analysis of Orbital Motions around Uniformly Rotating Irregular Asteroids By Xiyun HoU, ) Daniel J. SCHEERES, ) Xiaosheng XIN, ) Jinglang FENG, ) Jingshi TANG, ) Lin LIU, ) ) Shool of Astronomy
More informationThe Concept of Mass as Interfering Photons, and the Originating Mechanism of Gravitation D.T. Froedge
The Conept of Mass as Interfering Photons, and the Originating Mehanism of Gravitation D.T. Froedge V04 Formerly Auburn University Phys-dtfroedge@glasgow-ky.om Abstrat For most purposes in physis the onept
More informationpss Unusual evolution of the magnetism on oxygen in La 1 x Sr x CoO 3 solidi status physica
Phys. Status Solidi C, No., 54 58 (3) / DOI./pss. Unusual evolution of the magnetism on oxygen in La x Sr x CoO 3 physia pss urrent topis in solid state physis Sott Medling *,,Y.Lee, H. Zheng 3, J. F.
More informationOn the Quantum Theory of Radiation.
Physikalishe Zeitshrift, Band 18, Seite 121-128 1917) On the Quantum Theory of Radiation. Albert Einstein The formal similarity between the hromati distribution urve for thermal radiation and the Maxwell
More informationThe Unified Geometrical Theory of Fields and Particles
Applied Mathematis, 014, 5, 347-351 Published Online February 014 (http://www.sirp.org/journal/am) http://dx.doi.org/10.436/am.014.53036 The Unified Geometrial Theory of Fields and Partiles Amagh Nduka
More informationNon-Markovian study of the relativistic magnetic-dipole spontaneous emission process of hydrogen-like atoms
NSTTUTE OF PHYSCS PUBLSHNG JOURNAL OF PHYSCS B: ATOMC, MOLECULAR AND OPTCAL PHYSCS J. Phys. B: At. Mol. Opt. Phys. 39 ) 7 85 doi:.88/953-75/39/8/ Non-Markovian study of the relativisti magneti-dipole spontaneous
More informationAngular Distribution of Photoelectrons during Irradiation of Metal Surface by Electromagnetic Waves
Journal of Modern Physis, 0,, 780-786 doi:0436/jmp0809 Published Online August 0 (http://wwwsirporg/journal/jmp) Angular Distribution of Photoeletrons during Irradiation of Metal Surfae by letromagneti
More informationCOMPLEX INDUCTANCE AND ITS COMPUTER MODELLING
Journal of ELECTRICAL ENGINEERING, VOL. 53, NO. 1-2, 22, 24 29 COMPLEX INDUCTANCE AND ITS COMPUTER MODELLING Daniel Mayer Bohuš Ulryh The paper introdues the onept of the omplex indutane as a parameter
More informationDr G. I. Ogilvie Lent Term 2005
Aretion Diss Mathematial Tripos, Part III Dr G. I. Ogilvie Lent Term 2005 1.4. Visous evolution of an aretion dis 1.4.1. Introdution The evolution of an aretion dis is regulated by two onservation laws:
More informationModeling of Threading Dislocation Density Reduction in Heteroepitaxial Layers
A. E. Romanov et al.: Threading Disloation Density Redution in Layers (II) 33 phys. stat. sol. (b) 99, 33 (997) Subjet lassifiation: 6.72.C; 68.55.Ln; S5.; S5.2; S7.; S7.2 Modeling of Threading Disloation
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More informationWe consider the nonrelativistic regime so no pair production or annihilation.the hamiltonian for interaction of fields and sources is 1 (p
.. RADIATIVE TRANSITIONS Marh 3, 5 Leture XXIV Quantization of the E-M field. Radiative transitions We onsider the nonrelativisti regime so no pair prodution or annihilation.the hamiltonian for interation
More informationA model for measurement of the states in a coupled-dot qubit
A model for measurement of the states in a oupled-dot qubit H B Sun and H M Wiseman Centre for Quantum Computer Tehnology Centre for Quantum Dynamis Griffith University Brisbane 4 QLD Australia E-mail:
More informationWave Propagation through Random Media
Chapter 3. Wave Propagation through Random Media 3. Charateristis of Wave Behavior Sound propagation through random media is the entral part of this investigation. This hapter presents a frame of referene
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION doi:.8/nphys SUPPLEMENTARY INFORMATION for The Quantum-Optial Josephson Interferometer D. Gerae,, Hakan E. Türei, A. Imamoglu, V. Giovannetti, and Rosario Fazio, Institute of
More informationWavetech, LLC. Ultrafast Pulses and GVD. John O Hara Created: Dec. 6, 2013
Ultrafast Pulses and GVD John O Hara Created: De. 6, 3 Introdution This doument overs the basi onepts of group veloity dispersion (GVD) and ultrafast pulse propagation in an optial fiber. Neessarily, it
More informationFig Review of Granta-gravel
0 Conlusion 0. Sope We have introdued the new ritial state onept among older onepts of lassial soil mehanis, but it would be wrong to leave any impression at the end of this book that the new onept merely
More informationQUANTUM MECHANICS II PHYS 517. Solutions to Problem Set # 1
QUANTUM MECHANICS II PHYS 57 Solutions to Problem Set #. The hamiltonian for a lassial harmoni osillator an be written in many different forms, suh as use ω = k/m H = p m + kx H = P + Q hω a. Find a anonial
More informationA simple expression for radial distribution functions of pure fluids and mixtures
A simple expression for radial distribution funtions of pure fluids and mixtures Enrio Matteoli a) Istituto di Chimia Quantistia ed Energetia Moleolare, CNR, Via Risorgimento, 35, 56126 Pisa, Italy G.
More informationCritical Reflections on the Hafele and Keating Experiment
Critial Refletions on the Hafele and Keating Experiment W.Nawrot In 1971 Hafele and Keating performed their famous experiment whih onfirmed the time dilation predited by SRT by use of marosopi loks. As
More informationPhysics of Relaxation. Outline
Physis of Relaxation Weiguo Li Outline Fundamental relaxation Mehanisms Magneti dipole-dipole oupling» Stati oupling» Dynami oupling Frequeny dependene of relaxation Rate Temperature dependene of relaxation
More informationCollinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body Nakone Bello 1,a and Aminu Abubakar Hussain 2,b
International Frontier Siene Letters Submitted: 6-- ISSN: 9-8, Vol., pp -6 Aepted: -- doi:.8/www.sipress.om/ifsl.. Online: --8 SiPress Ltd., Switzerland Collinear Equilibrium Points in the Relativisti
More informationNuclear Shell Structure Evolution Theory
Nulear Shell Struture Evolution Theory Zhengda Wang (1) Xiaobin Wang () Xiaodong Zhang () Xiaohun Wang () (1) Institute of Modern physis Chinese Aademy of SienesLan Zhou P. R. China 70000 () Seagate Tehnology
More informationChapter 9. The excitation process
Chapter 9 The exitation proess qualitative explanation of the formation of negative ion states Ne and He in He-Ne ollisions an be given by using a state orrelation diagram. state orrelation diagram is
More informationThe Electromagnetic Radiation and Gravity
International Journal of Theoretial and Mathematial Physis 016, 6(3): 93-98 DOI: 10.593/j.ijtmp.0160603.01 The Eletromagneti Radiation and Gravity Bratianu Daniel Str. Teiului Nr. 16, Ploiesti, Romania
More informationOn Chaotic Cartesian Product of Graphs and Their Retractions
ISSN 749-3889 (print), 749-3897 (online) International Journal of Nonlinear Siene Vol.5(03) No.,pp.86-90 On Chaoti Cartesian Produt of Graphs and Their Retrations M. Abu-Saleem Department of Mathematis,
More informationTorus doubling resonances and breather stability
PHYSICAL REVIEW E 7, 61 Torus doubling resonances and breather stability L. S. Schulman* Physics Department, Clarkson University, Potsdam, New York 13699-5, USA and Max Planck Institute for the Physics
More informationControl Theory association of mathematics and engineering
Control Theory assoiation of mathematis and engineering Wojieh Mitkowski Krzysztof Oprzedkiewiz Department of Automatis AGH Univ. of Siene & Tehnology, Craow, Poland, Abstrat In this paper a methodology
More informationBrazilian Journal of Physics, vol. 29, no. 3, September, Classical and Quantum Mechanics of a Charged Particle
Brazilian Journal of Physis, vol. 9, no. 3, September, 1999 51 Classial and Quantum Mehanis of a Charged Partile in Osillating Eletri and Magneti Fields V.L.B. de Jesus, A.P. Guimar~aes, and I.S. Oliveira
More informationarxiv:cond-mat/ v1 [cond-mat.str-el] 3 Aug 2006
arxiv:ond-mat/0608083v1 [ond-mat.str-el] 3 Aug 006 Raman sattering for triangular latties spin- 1 Heisenberg antiferromagnets 1. Introdution F. Vernay 1,, T. P. Devereaux 1, and M. J. P. Gingras 1,3 1
More informationSURFACE WAVES OF NON-RAYLEIGH TYPE
SURFACE WAVES OF NON-RAYLEIGH TYPE by SERGEY V. KUZNETSOV Institute for Problems in Mehanis Prosp. Vernadskogo, 0, Mosow, 75 Russia e-mail: sv@kuznetsov.msk.ru Abstrat. Existene of surfae waves of non-rayleigh
More informationEffect of magnetization process on levitation force between a superconducting. disk and a permanent magnet
Effet of magnetization proess on levitation fore between a superonduting disk and a permanent magnet L. Liu, Y. Hou, C.Y. He, Z.X. Gao Department of Physis, State Key Laboratory for Artifiial Mirostruture
More informationRelativity in Classical Physics
Relativity in Classial Physis Main Points Introdution Galilean (Newtonian) Relativity Relativity & Eletromagnetism Mihelson-Morley Experiment Introdution The theory of relativity deals with the study of
More informationUNCERTAINTY RELATIONS AS A CONSEQUENCE OF THE LORENTZ TRANSFORMATIONS. V. N. Matveev and O. V. Matvejev
UNCERTAINTY RELATIONS AS A CONSEQUENCE OF THE LORENTZ TRANSFORMATIONS V. N. Matveev and O. V. Matvejev Joint-Stok Company Sinerta Savanoriu pr., 159, Vilnius, LT-315, Lithuania E-mail: matwad@mail.ru Abstrat
More informationClassical Trajectories in Rindler Space and Restricted Structure of Phase Space with PT-Symmetric Hamiltonian. Abstract
Classial Trajetories in Rindler Spae and Restrited Struture of Phase Spae with PT-Symmetri Hamiltonian Soma Mitra 1 and Somenath Chakrabarty 2 Department of Physis, Visva-Bharati, Santiniketan 731 235,
More informationThe A T emission of KCl:Tl interpreted as a double A T +A X emission
The A T emission of KCl:Tl interpreted as a double A T +A X emission D. Mugnai, G. P. Pazzi, P. Fabeni, and A. Ranfagni Nello Carrara Institute of Applied Physics, CNR Florence Research Area, Via Madonna
More informationThe simulation analysis of the bridge rectifier continuous operation in AC circuit
Computer Appliations in Eletrial Engineering Vol. 4 6 DOI 8/j.8-448.6. The simulation analysis of the bridge retifier ontinuous operation in AC iruit Mirosław Wiślik, Paweł Strząbała Kiele University of
More informationDiscontinuity of Shannon information entropy for two-electron atoms
Chemial Physis 39 (25) 127 131 www.elsevier.om/loate/hemphys Disontinuity of Shannon information entropy for two-eletron atoms Qiun Shi, Sabre Kais * Department of Chemistry, Purdue University, 1393 Brown
More informationarxiv: v1 [physics.gen-ph] 5 Jan 2018
The Real Quaternion Relativity Viktor Ariel arxiv:1801.03393v1 [physis.gen-ph] 5 Jan 2018 In this work, we use real quaternions and the basi onept of the final speed of light in an attempt to enhane the
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationCRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS
Russian Physis Journal, Vol. 48, No. 8, 5 CRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS A. N. Taskin, V. N. Udodov, and A. I. Potekaev UDC
More informationSpectroscopic Signatures of Novel Oxygen-Defect Complexes in Stoichiometrically Controlled CdSe
Physis Physis Researh Publiations Purdue University Year 008 Spetrosopi Signatures of Novel Oxygen-Defet Complexes in Stoihiometrially Controlled CdSe G. Chen J. S. Bhosale I. Miotkowski A. K. Ramdas This
More informationCALCULATION OF NONLINEAR TUNE SHIFT USING BEAM POSITION MEASUREMENT RESULTS
International Journal of Modern Physis A Vol. 24, No. 5 (2009) 974 986 World Sientifi Publishing Company CALCULATION OF NONLINEAR TUNE SHIFT USING BEAM POSITION MEASUREMENT RESULTS PAVEL SNOPOK, MARTIN
More informationMonte Carlo Simulation of Electron and Radiative Emission from Silicon Diodes
SIMULATION OF SEMICONDUCTOR DEVICES AND PROCESSES Vol. 4 Edited by W. Fihtner, D. Aemmer - Zurih (Switzerland) September 12-14,1991 - Hartung-Gorre 521 Monte Carlo Simulation of Eletron and Radiative Emission
More informationGeneral Equilibrium. What happens to cause a reaction to come to equilibrium?
General Equilibrium Chemial Equilibrium Most hemial reations that are enountered are reversible. In other words, they go fairly easily in either the forward or reverse diretions. The thing to remember
More informationElectromagnetic radiation of the travelling spin wave propagating in an antiferromagnetic plate. Exact solution.
arxiv:physis/99536v1 [physis.lass-ph] 15 May 1999 Eletromagneti radiation of the travelling spin wave propagating in an antiferromagneti plate. Exat solution. A.A.Zhmudsky November 19, 16 Abstrat The exat
More information(E B) Rate of Absorption and Stimulated Emission. π 2 E 0 ( ) 2. δ(ω k. p. 59. The rate of absorption induced by the field is. w k
p. 59 Rate of Absorption and Stimulated Emission The rate of absorption indued by the field is π w k ( ω) ω E 0 ( ) k ˆ µ δω ( k ω) The rate is learly dependent on the strength of the field. The variable
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 16 Aug 2004
Computational omplexity and fundamental limitations to fermioni quantum Monte Carlo simulations arxiv:ond-mat/0408370v1 [ond-mat.stat-meh] 16 Aug 2004 Matthias Troyer, 1 Uwe-Jens Wiese 2 1 Theoretishe
More informationParticle-wave symmetry in Quantum Mechanics And Special Relativity Theory
Partile-wave symmetry in Quantum Mehanis And Speial Relativity Theory Author one: XiaoLin Li,Chongqing,China,hidebrain@hotmail.om Corresponding author: XiaoLin Li, Chongqing,China,hidebrain@hotmail.om
More information11.4 Molecular Orbital Description of the Hydrogen Molecule Electron Configurations of Homonuclear Diatomic Molecules
Chap Moleular Eletroni Struture Table of Contents. The orn-oppenheimer pproximation -. The Hydrogen Moleule Ion.3 Calulation of the Energy of the Hydrogen Moleule Ion.4 Moleular Orbital Desription of the
More informationarxiv: v1 [physics.optics] 18 Aug 2015
Variale frequeny photoni rystals Xiang-Yao Wu a, Ji Ma a, Xiao-Jing Liu a Jing-Hai Yang a, Hong Li a and Wan-Jin Chen a a Institute of Physis, Jilin Normal University, Siping 136000 China arxiv:1508.04299v1
More informationGravitomagnetic Effects in the Kerr-Newman Spacetime
Advaned Studies in Theoretial Physis Vol. 10, 2016, no. 2, 81-87 HIKARI Ltd, www.m-hikari.om http://dx.doi.org/10.12988/astp.2016.512114 Gravitomagneti Effets in the Kerr-Newman Spaetime A. Barros Centro
More informationIII. SURFACE PROPERTIES III.A. SURFACE TENSION SURFACE PROPERTIES
III. SURFACE PROPERTIES III.A. SURFACE TENSION GOAL: To investigate the influene of the solution onentration and/or the kind of the solute on the surfae tension INTRODUCTION Liquids tend to adopt shapes
More informationUTC. Engineering 329. Proportional Controller Design. Speed System. John Beverly. Green Team. John Beverly Keith Skiles John Barker.
UTC Engineering 329 Proportional Controller Design for Speed System By John Beverly Green Team John Beverly Keith Skiles John Barker 24 Mar 2006 Introdution This experiment is intended test the variable
More informationELECTROCHEMISTRY Lecture/Lession Plan -1
Chapter 4 ELECTROCHEMISTRY Leture/Lession Plan -1 ELECTROCHEMISTRY 4.1 Conept of eletrohemistry Eletrohemistry is a branh of hemistry where we will study how hemial energy an be transformed into eletrial
More informationModels for the simulation of electronic circuits with hysteretic inductors
Proeedings of the 5th WSEAS Int. Conf. on Miroeletronis, Nanoeletronis, Optoeletronis, Prague, Czeh Republi, Marh 12-14, 26 (pp86-91) Models for the simulation of eletroni iruits with hystereti indutors
More informationSupporting Information for
Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 Supporting Information for Exitation polarization modulation in loalization mirosopy allows to resolve
More informationAharonov-Bohm effect. Dan Solomon.
Aharonov-Bohm effet. Dan Solomon. In the figure the magneti field is onfined to a solenoid of radius r 0 and is direted in the z- diretion, out of the paper. The solenoid is surrounded by a barrier that
More informationIMPACT MODELLING OF THE COEFFICIENT OF RESTITUTION OF POTATOES BASED ON THE KELVIN- VOIGHT PAIR
Bulletin of the Transilvania University of Braşov Series II: Forestry Wood Industry Agriultural Food Engineering Vol. 9 (58) No. - 06 IMPACT MODELLING OF THE COEFFICIENT OF RESTITUTION OF POTATOES BASED
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationMean Activity Coefficients of Peroxodisulfates in Saturated Solutions of the Conversion System 2NH 4. H 2 O at 20 C and 30 C
Mean Ativity Coeffiients of Peroxodisulfates in Saturated Solutions of the Conversion System NH 4 Na S O 8 H O at 0 C and 0 C Jan Balej Heřmanova 5, 170 00 Prague 7, Czeh Republi balejan@seznam.z Abstrat:
More informationarxiv:physics/ v1 [physics.class-ph] 8 Aug 2003
arxiv:physis/0308036v1 [physis.lass-ph] 8 Aug 003 On the meaning of Lorentz ovariane Lszl E. Szab Theoretial Physis Researh Group of the Hungarian Aademy of Sienes Department of History and Philosophy
More informationThe shape of a hanging chain. a project in the calculus of variations
The shape of a hanging hain a projet in the alulus of variations April 15, 218 2 Contents 1 Introdution 5 2 Analysis 7 2.1 Model............................... 7 2.2 Extremal graphs.........................
More informationTemperature dependence of anomalous luminescence decay:
PHYSICAL REVIEW B 66, 155102 2002 Temperature dependence of anomalous luminescence decay: Theory and experiment E. Mihóková, 1, * L. S. Schulman, 2 M. Nikl, 1 B. Gaveau, 3 K. Polák, 1 K. Nitsch, 1 and
More informationSTUDY OF INTERFACIAL BEHAVIOR OF CNT/POLYMER COMPOSITE BY CFE METHOD
THE 19TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS STUDY OF INTERFACIAL BEHAVIOR OF CNT/POLYMER COMPOSITE BY CFE METHOD Q. S. Yang*, X. Liu, L. D. Su Department of Engineering Mehanis, Beijing University
More informationOn refinement of certain laws of classical electrodynamics
On refinement of ertain laws of lassial eletrodynamis http://fmnauka.narod.ru/works.html F. F. Mende Abstrat mende_fedor@mail.ru In the ontemporary lassial eletrodynamis exists many unresolved problems.
More information). In accordance with the Lorentz transformations for the space-time coordinates of the same event, the space coordinates become
Relativity and quantum mehanis: Jorgensen 1 revisited 1. Introdution Bernhard Rothenstein, Politehnia University of Timisoara, Physis Department, Timisoara, Romania. brothenstein@gmail.om Abstrat. We first
More informationGravitation is a Gradient in the Velocity of Light ABSTRACT
1 Gravitation is a Gradient in the Veloity of Light D.T. Froedge V5115 @ http://www.arxdtf.org Formerly Auburn University Phys-dtfroedge@glasgow-ky.om ABSTRACT It has long been known that a photon entering
More informationSTATISTICAL MECHANICS & THERMODYNAMICS
UVA PHYSICS DEPARTMENT PHD QUALIFYING EXAM PROBLEM FILE STATISTICAL MECHANICS & THERMODYNAMICS UPDATED: NOVEMBER 14, 212 1. a. Explain what is meant by the density of states, and give an expression for
More informationThe Effectiveness of the Linear Hull Effect
The Effetiveness of the Linear Hull Effet S. Murphy Tehnial Report RHUL MA 009 9 6 Otober 009 Department of Mathematis Royal Holloway, University of London Egham, Surrey TW0 0EX, England http://www.rhul.a.uk/mathematis/tehreports
More informationTWO WAYS TO DISTINGUISH ONE INERTIAL FRAME FROM ANOTHER
TWO WAYS TO DISTINGUISH ONE INERTIAL FRAME FROM ANOTHER (WHY IS THE SPEED OF LIGHT CONSTANT?) Dr. Tamas Lajtner Correspondene via web site: www.lajtnemahine.om. ABSTRACT... 2 2. SPACETIME CONTINUUM BY
More informationIntegration of the Finite Toda Lattice with Complex-Valued Initial Data
Integration of the Finite Toda Lattie with Complex-Valued Initial Data Aydin Huseynov* and Gusein Sh Guseinov** *Institute of Mathematis and Mehanis, Azerbaijan National Aademy of Sienes, AZ4 Baku, Azerbaijan
More informationLecture 15 (Nov. 1, 2017)
Leture 5 8.3 Quantum Theor I, Fall 07 74 Leture 5 (Nov., 07 5. Charged Partile in a Uniform Magneti Field Last time, we disussed the quantum mehanis of a harged partile moving in a uniform magneti field
More informationDetermination of the reaction order
5/7/07 A quote of the wee (or amel of the wee): Apply yourself. Get all the eduation you an, but then... do something. Don't just stand there, mae it happen. Lee Iaoa Physial Chemistry GTM/5 reation order
More informationCavity flow with surface tension past a flat plate
Proeedings of the 7 th International Symposium on Cavitation CAV9 Paper No. ## August 7-, 9, Ann Arbor, Mihigan, USA Cavity flow with surfae tension past a flat plate Yuriy Savhenko Institute of Hydromehanis
More informationthe following action R of T on T n+1 : for each θ T, R θ : T n+1 T n+1 is defined by stated, we assume that all the curves in this paper are defined
How should a snake turn on ie: A ase study of the asymptoti isoholonomi problem Jianghai Hu, Slobodan N. Simić, and Shankar Sastry Department of Eletrial Engineering and Computer Sienes University of California
More informationMetric of Universe The Causes of Red Shift.
Metri of Universe The Causes of Red Shift. ELKIN IGOR. ielkin@yande.ru Annotation Poinare and Einstein supposed that it is pratially impossible to determine one-way speed of light, that s why speed of
More informationEXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION
Journal of Mathematial Sienes: Advanes and Appliations Volume 3, 05, Pages -3 EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION JIAN YANG, XIAOJUAN LU and SHENGQIANG TANG
More informationSupplementary information for: All-optical signal processing using dynamic Brillouin gratings
Supplementary information for: All-optial signal proessing using dynami Brillouin gratings Maro Santagiustina, Sanghoon Chin 2, Niolay Primerov 2, Leonora Ursini, Lu Thévena 2 Department of Information
More informationMODELING MATTER AT NANOSCALES. 4. Introduction to quantum treatments Eigenvectors and eigenvalues of a matrix
MODELING MATTER AT NANOSCALES 4 Introdution to quantum treatments 403 Eigenvetors and eigenvalues of a matrix Simultaneous equations in the variational method The problem of simultaneous equations in the
More informationPHY 108: Optical Physics. Solution to Midterm Test
PHY 108: Optial Physis Solution to Midterm Test TA: Xun Jia 1 May 14, 2008 1 Email: jiaxun@physis.ula.edu Spring 2008 Physis 108 Xun Jia (May 14, 2008) Problem #1 For a two mirror resonant avity, the resonane
More informationDynamics of the Electromagnetic Fields
Chapter 3 Dynamis of the Eletromagneti Fields 3.1 Maxwell Displaement Current In the early 1860s (during the Amerian ivil war!) eletriity inluding indution was well established experimentally. A big row
More informationExtending LMR for anisotropic unconventional reservoirs
Extending LMR for anisotropi unonventional reservoirs Maro A. Perez Apahe Canada Ltd Summary It has beome inreasingly advantageous to haraterize rok in unonventional reservoirs within an anisotropi framework.
More informationUPPER-TRUNCATED POWER LAW DISTRIBUTIONS
Fratals, Vol. 9, No. (00) 09 World Sientifi Publishing Company UPPER-TRUNCATED POWER LAW DISTRIBUTIONS STEPHEN M. BURROUGHS and SARAH F. TEBBENS College of Marine Siene, University of South Florida, St.
More informationWe will show that: that sends the element in π 1 (P {z 1, z 2, z 3, z 4 }) represented by l j to g j G.
1. Introdution Square-tiled translation surfaes are lattie surfaes beause they are branhed overs of the flat torus with a single branhed point. Many non-square-tiled examples of lattie surfaes arise from
More information