Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ ₀〉 = cos α | 10〉 + sin α | 01〉 and | ? ₀〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C _ij × C _ik × C _il , where C _mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C _ij × C _kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.     

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.     

Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

We consider the Ising model on a dense Erd?s–Rényi random graph, \({\mathcal {G}}(N,p)\), with \(p>0\) fixed—equivalently, a disordered Curie–Weiss Ising model with \(\hbox {Ber}(p)\) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of \({\mathcal {G}}(N,p)\) with \(p>0\) fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.     

Dynamics of Bose-Condensed Ultracold Atoms and Trimer Molecules with the Formation of Atomic–Molecular Pairs

Journal of Experimental and Theoretical Physics - The results of investigation of the photodissociation dynamics of triatomic Bose-condensed ultracold molecules (trimers) with the formation of...     

Microcanonical Analysis of the Curie–Weiss Anisotropic Quantum Heisenberg Model in a Magnetic Field

The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying the concavity properties of entropies. The microcanonical entropy \(s(e,\varvec{m})\) is obtained as a function of the energy \(e\) and the magnetization vector \({\varvec{m}}\) in the thermodynamic limit. Since, for this model, \(e\) is uniquely determined by \({\varvec{m}}\) , the same information can be encoded either in \(s(\varvec{m})\) or \(s(e,m_1,m_2)\) . Although these two entropies correspond to the same physical setting of fixed \(e\) and \({\varvec{m}}\) , their concavity properties differ. The entropy \(s_{{\varvec{h}}}(u)\) , describing the model at fixed total energy \(u\) and in a homogeneous external magnetic field \({\varvec{h}}\) of arbitrary direction, is obtained by reduction from the nonconcave entropy \(s(e,m_1,m_2)\) . In doing so, concavity, and therefore equivalence of ensembles, is restored. \(s_{{\varvec{h}}}(u)\) has nonanalyticities on surfaces of co-dimension 1 in the \((u,\varvec{h})\) -space. Projecting these surfaces into lower-dimensional phase diagrams, we observe that the resulting phase transition lines are situated in the positive-temperature region for some parameter values, and in the negative-temperature region for others. In the canonical setting of a system coupled to a heat bath of positive temperatures, the nonanalyticities in the microcanonical negative-temperature region cannot be observed, and this leads to a situation of effective nonequivalence even when formal equivalence holds.     

Open M-shell Opacity of Bromine Plasma in Comparison of the Detailed Level Accounting Model with the Average Atom Model

The open M-shell opacity of a hot bromine plasma has been calculated by using a detailed level accounting （DLA） model. One-electron orbitals obtained by solving the fully relativistic Dirac-Fock equations are used to obtain the atomic levels and the radiative transition oscillator strengths. Only the level mixing within the same electron configuration is considered to reduce the complexity of the calculations. Detailed comparisons have been made between the results of the DLA and average atom （AA） models. Good agreements are found for both the M-shell transition arrays and the Planck mean opacity but there are differences for the line positions in the 2p → 3d absorption region due to the statistical treatment for the one-electron orbitals in the AA model.     

Analysis of the Electrohydrodynamic Flow in a Symmetric System of Electrodes by the Method of Dynamic Current–Voltage Characteristics

We have solved the problem of injection-type through electrohydrodynamic (EHD) flow in a closed channel. We have considered a model of a liquid with four types of ions. It is shown that a through EHD flow without internal vortices in the electrode gap is formed for the ratio 2 : 1 of the initial injection current from the electrodes in the channel. The structure of the flow in different parts of the channel and the integral characteristics of the flow have been analyzed. It is shown that for a quadratic function of injection at the electrodes, the current–voltage characteristic of the flow is also quadratic.     

Dissipation of System and Atom in Two-Photon Jaynes–Cummings Model with Degenerate Atomic Levels

A method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes–Cummings model (JCM) with degenerate atomic levels. The numerical results show that the degeneracy of atomic levels prolongs the period of entanglement between the atom and the field. The asymptotic value of atomic linear entropy is apparently increased by the degeneration. The amplitude of local entanglement and disentanglement is suppressed. The better the initial coherence property of the degenerate atom, the larger the coherence loss.     

Mechanisms of Avalanche Dynamics in a Stochastic Four-State Sandpile Model

We study the stochastic four-state sandpile model on the square lattice. The static and dynamical properties of the model are investigated and compared with the deterministic sandpile model of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59 (1987) 381]. The numerical results show that the stochastic model defines a new universality class with respect to the deterministic sandpile. We also find that the waves in an avalanche are uncorrelated in the stochastic model (in the BTW model, the waves in an avalanche are correlated). The physical origin of the critical behaviour of the stochastic model being different from that of the BTW model is ascribed to the ordering and deterministic property of the toppling law in the BTW model.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.     

Molecular Dynamics Simulations of Ti Crystallization with Solid–Liquid Configuration Method

Physics of the Solid State - The computation models were created with the solid-liquid configuration method. The molecular dynamics simulations were performed to exhibit the crystallization process...     

Flocking of the Motsch–Tadmor Model with a Cut-Off Interaction Function

In this paper, we study the flocking behavior of the Motsch–Tadmor model with a cut-off interaction function. Our analysis shows that connectedness is important for flocking of this kind of model. Fortunately, we get a sufficient condition imposed only on the model parameters and initial data to guarantee the connectedness of the neighbor graph associated with the system. Then we present a theoretical analysis for flocking, and show that the system achieves consensus at an exponential rate.     

Analysis of Experimental Results by the Havriliak–Negami Model in Dielectric Spectroscopy

The problem of identifying experimental results on studying frequency dependences of the real and imaginary parts of dielectric permittivity concerning the correspondence to one of accepted frequency dispersion models: Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami models is considered. Based on expressions for components of complex dielectric permittivity with the use of mathematical analysis, a sequence of steps for the determination of the following characteristic parameters of the generalized Havriliak–Negami model is developed: static ε _S and high-frequency ε_∞ dielectric permittivity, frequency dispersion indices α and β, and relaxation time τ. As an example, the parameters ε _S , ε_∞, α, β, and τ are calculated for a sample of a frozen disperse medium based on fine-grained quartz powder at a humidity of 13% in a temperature range from –140 to 0°C.     

Analysis of Polaron Band Formation with the One-Dimensional Holstein Model

We present an analytic result of the polaronic band structure by using the one-dimensional Holstein model on an infinite lattice. The single-phonon effect is used to investigate the ground state properties, such as the polaronic band structure, ground state energy, phonon distribution and effective mass, which agree with the numerical and analytic results obtained recently in the region from the weak coupling to the intermediate coupling.     

Application to Rat Lung of the Extended Rorschach–Hazlewood Model of Spin–Lattice Relaxation

The spin–lattice relaxation timeT₁was measured in excised degassed (airless) rat lungs over the frequency range 6.7 to 80.5 MHz. The observed frequency dependence was fitted successfully to the water–biopolymer cross-relaxation theory proposed by H. E. Rorschach and C. F. Hazlewood (RH) [J. Magn. Reson.70,79 (1986)]. The rotating frame spin–lattice relaxation timeT_1ρwas also measured in rat lung fragments over the frequency range 0.56 to 5.6 kHz, and the observed frequency dependence was explained with an extension of the RH model. The agreement between the theory and the experimental data in both cases is good.     

Analysis of Near-Field Diffraction Pattern of a Metallic Probe Tip with the Boundary Diffraction Wave Method

The boundary diffraction wave theory is introduced to analyse a near-field diffraction （NFD） pattern of a metallic probe tip of apertureless scanning near-field microscopy. This method is simple and can give a clear physical picture. The polarization effect of the incident light and the different shapes of the metallic probe tip are simulated. The results show that the NFD pattern of the metallic probe tip is directly related to those factors.     

Relaxation of the magnetic state of a ferromagnetic–superconducting layered structure

We have proposed a real-time method of neutron reflectometry. The magnetic state of the Ta/V/FM/Nb/Si ferromagnetic–superconducting system has been analyzed. Relaxation of the inhomogeneous magnetic state with a characteristic time of several hours, which depends on the magnetic field magnitude and temperature, has been observed. The relaxation of the domain structure has changed upon a transition of the V and Nb layers to the superconducting state. It has been concluded that real-time reflectometry data for polarized neutrons are important for determining the origin of magnetism in ferromagnetic–superconducting layered structures.     

Phase Diagram of the BCS–Hubbard Model in a Magnetic Field

We propose an extended BCS–Hubbard model and investigate its ground state phase diagram in an external magnetic field. By mapping the model onto a model of spinless fermions coupled with conserving Z₂ variables which are mimicked by pseudospins, the model is shown to be exactly solvable along the symmetric lines for an arbitrary on-site Hubbard interaction on the bipartite lattice. In the zero field limit, the ground states exhibit an antiferromagnetic order of pseudospins. In the lar...     

Atomic mobility in a ternary liquid Ga–In–Sn alloy of the eutectic composition

The nuclear spin–lattice relaxation and Knight shift of ⁷¹Ga, ⁶⁹Ga, and ¹¹⁵In nuclei in a ternary liquid gallium–indium–tin alloy of the eutectic composition, which was introduced into pores of an opal matrix and porous glasses with pore sizes of 18 and 7 nm, have been investigated and compared with those for the bulk melt. It has been found that longitudinal relaxation is accelerated and the Knight shift is decreased, depending on the size of pores. The correlation time of the atomic motion has been calculated for the nanostructured melt in porous matrices. It has been shown that the atomic mobility in the melt decreases with decreasing size of pores in the glasses.

     

Adomyan Decomposition Method for a Two-Component Nonlocal Reaction-Diffusion Model of the Fisher–Kolmogorov–Petrovsky–Piskunov Type

Russian Physics Journal - We consider an approach to constructing approximate analytical solutions for the one-dimensional twocomponent reaction-diffusion model describing the dynamics of...