arXiv subjects

Andrey Pereverzev

Publications and source records attributed to Andrey Pereverzev.

17 recordsLinked to original sources

arXiv2026

Lattice thermal conductivity decomposition: Peierls vs. non-Peierls contributions

The Green-Kubo lattice thermal conductivity computed using the full classical heat current of a crystalline solid is compared with results obtained from the quadratic component of the heat current and from the commonly used Peierls heat current. In addition, thermal conductivity within the relaxation time approximation is evaluated. Three crystalline systems are investigated: solid argon, a model of solid argon with alternating masses, and $α$-quartz. For all materials considered, the thermal conductivities calculated using the quadratic and Peierls heat currents differ only slightly. In the case of $α$-quartz, the optical phonon contribution to the thermal conductivity is found to exceed that of the acoustic modes. The relaxation time approximation systematically underestimates the thermal conductivity in all three systems.

cond-mat.mtrl-sci↗

arXiv2025

On the definition of heat current for periodic systems and its implications for simulations of thermal conductivity in solids

We re-derive the expression for the heat current for a classical system subject to periodic boundary conditions and show that it can be written as a sum of two terms. The first term is a time derivative of the first moment of the system energy density while the second term is expressed through the energy transfer rate through the periodic boundary. We show that in solids the second term alone leads to the same thermal conductivity as the full expression for the heat current when used in the Green-Kubo approach. More generally, energy passing though any surface formed by translation of the original periodic boundary can be used to calculate thermal conductivity. These statements are verified for two systems: crystalline argon and crystals of argon and krypton forming an interface.

cond-mat.stat-mech↗

arXiv2023

Molecular dynamics study of diffusionless phase transformations in HMX: $β$-HMX twinning and $β$-$ε$ phase transition

We use molecular dynamics to study mechanism of deformation twinning of $β$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($β$-HMX) in the $P2_1/n$ space group setting for the twin system specified by $K_1=(101)$, $η_1=[10\overline{1}]$, $K_2=(10\overline{1})$, and $η_2=[101]$ at $T=1$ K and 300 K. Twinning of a single perfect crystal was induced by imposing increasing stress. The following three forms of stress were considered: uniaxial compression along $[001]$, shear stress in $K_1$ plane along $η_1$ direction, and shear stress in $K_2$ plane along $η_2$ direction. In all cases the crystal transforms to its twin by the same mechanism: as the stress increases, the $a$ and $c$ lattice parameters become, respectively, longer and shorter; soon after the magnitude of $a$ exceeds that of $c$ the system undergoes a quick phase-transition-like transformation. This transformation can be approximately separated into two stages: glide of the essentially intact $\{101\}$ crystal planes along $\langle10\overline{1}\rangle$ crystal directions followed by rotations of all HMX molecules accompanied by N-NO$_2$ and CH$_2$ group rearrangements. The overall process corresponds to a military transformation. If uniaxial compression along $[001]$ is applied to a $β$-HMX crystal which is already subject to a hydrostatic pressure $\gtrsim 10$ GPa, the transformation described above proceeds through the crystal-plane gliding stage but only minor molecular rearrangements occurs. This results in a high-pressure phase of HMX which belongs to the $P2_1/n$ space group. The coexistence curve for this high-pressure phase and $β$-HMX is constructed using the harmonic approximation for the crystal Hamiltonians.

cond-mat.mtrl-sci↗

arXiv2023

Thermal conductivity tensor of $β$-HMX as a function of pressure and temperature from equilibrium molecular dynamics simulations

We apply the Green-Kubo (G-K) approach to obtain the thermal conductivity tensor of $β$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($β$-HMX) as a function of pressure and temperature from equilibrium molecular dynamics (MD) simulations. Direct application of the G-K formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) accumulated simulation times. To partially mitigate this slow convergence, we apply a recently implemented numerical procedure [Int. J. Heat Mass Trans. 188, 122647 (2022)] that involves physically justified filtering of the MD-calculated G-K heat current and fitting the integrated time-dependent thermal conductivity to a physically motivated double-exponential function. The thermal conductivity tensor was determined for pressures 1 atm $ \leq P \leq $ 30 GPa and temperatures 300 K $\leq T \leq$ 900 K. The thermal conductivity $κ^{αβ} (T,P)$ increases with increasing pressure, by approximately an order of magnitude over the interval considered, and decreases with increasing temperature. The MD predictions are compared to experimental and other theoretically determined values for the thermal conductivity of $β$-HMX. A simple, semi-empirical fitting form is proposed that captures the behavior of $κ^{αα} (T,P)$ over the pressure and temperature intervals studied.

cond-mat.mtrl-sci↗

arXiv2022

Isothermal and adiabatic elastic constants from virial fluctuations

We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential energies of atomic groups that make up the total potential energy. It is shown that in the thermodynamic limit, the Born term, which depends on the second derivatives of potential energy, can be expressed exactly in terms of equilibrium averages that involve two types of atomic-group virials. As a result, the new form of the Born term involves only first derivatives of either atomic-group or total potential energies. The derived elastic constant expressions involving the two forms of the Born terms are tested and compared using molecular-dynamics simulations of crystalline argon and silicon. For both materials, the elastic constants obtained using the two forms of the Born term are in good agreement. In particular, the new form of the Born term converges to the same value as the original Born term but at a slower rate. The results for silicon also agree well with the results from the previous molecular-dynamics studies.

cond-mat.mtrl-sci↗

arXiv2022

Heat-current filtering for Green-Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal $β$-HMX

The closely related Green-Kubo and Helfand moment approaches are applied to obtain the thermal conductivity tensor of $β$-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane ($β$-HMX) at $T=300$ K and $P=1$ atm from equilibrium molecular dynamics (MD) simulations. Direct application of the Green-Kubo formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) simulation times. To partially mitigate this slow convergence we developed a numerical procedure that involves filtering of the MD-calculated heat current. The filtering is accomplished by physically justified removal of the heat-current component which is given by a linear function of atomic velocities. A double-exponential function is fitted to the integrated time-dependent thermal conductivity, calculated using the filtered current, to obtain the asymptotic values for the thermal conductivity. In the Helfand moment approach the thermal conductivity is obtained from the rates of change of the averaged squared Helfand moments. Both methods are applied to periodic $β$-HMX supercells of four different sizes and estimates for the thermal conductivity of the infinitely large crystal are obtained using Matthiessen's rule. Both approaches yield similar although not identical thermal conductivity values. These predictions are compared to experimental and other theoretically determined values for the thermal conductivity of $β$-HMX.

cond-mat.mtrl-sci↗

arXiv2021

On the derivation of exact eigenstates of the generalized squeezing operator

We construct the states that are invariant under the action of the generalized squeezing operator $\exp{(z{a^{\dagger k}}-z^*a^k)}$ for arbitrary positive integer $k$. The states are given explicitly in the number representation. We find that for a given value of $k$ there are $k$ such states. We show that the states behave as $n^{-k/4}$ when occupation number $n\to\infty$. This implies that for any $k\geq3$ the states are normalizable. For a given $k$, the expectation values of operators of the form $(a^{\dagger} a)^j$ are finite for positive integer $j < (k/2-1)$ but diverge for integer $j\geq (k/2-1)$. For $k=3$ we also give an explicit form of these states in the momentum representation in terms of Bessel functions.

quant-ph↗

arXiv2008

Hamiltonian approach for the wave packet dynamics: Beyond Gaussian wave functions

It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential.

quant-ph↗

arXiv2008

Electron transfer dynamics using projected modes

For electron-phonon Hamiltonians with the couplings linear in the phonon operators we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of freedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. We show that for the $n$-level electronic system the minimum number of modes in the first group is $n_s=(n^2+n-2)/2$. The separation of the normal modes into two groups allows one to develop new approximation schemes. We apply one of such schemes to study exitonic relaxation in a model semiconducting molecular heterojuction.

cond-mat.mtrl-sci↗

arXiv2006

Time-convolutionless master equation dynamics for charge-transfer processes between semiconducting polymers

We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not applicable. Here we apply the approach to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to an Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers. In this later system, we show how both slow and fast phonon modes contribute to the decay of an exciton across a heterojunction interface.

cond-mat.mtrl-sci↗

arXiv2006

Time-convolutionless master equation for mesoscopic electron-phonon systems

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

cond-mat.mtrl-sci↗

arXiv2006

Constraints on the two-particle distribution function due to the permutational symmetry of the higher order distribution functions

We investigate how the range of parameters that specify the two-particle distribution function is restricted if we require that this function be obtained from the $n^{\rm th}$ order distribution functions that are symmetric with respect to the permutation of any two particles. We consider the simple case when each variable in the distribution functions can take only two values. Results for all $n$ values are given, including the limit of $n\to\infty$. We use our results to obtain bounds on the allowed values of magnetization and magnetic susceptibility in an $n$ particle Fermi fluid.

cond-mat.stat-mech↗

arXiv2005

Exactly solvable approximating models for Rabi Hamiltonian dynamics

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

quant-ph↗

arXiv2005

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.

cond-mat.stat-mech↗

arXiv2003

Least paradoxical states of the Schrödinger cat

Modeling the Schrödinger cat by a two state system and assuming that the cat is coupled to the environment we look for the least paradoxical states of the Schrödinger cat in the following way. We require the reduced density matrix of the cat for one of the two states in the superposition to be the same as the one for the total state while distinct from the reduced density matrix of the cat for the other state in the superposition. We then look for the reduced density matrices for which the cat is as alive as possible for the first state (and as dead as possible for the second state). The resulting states are those in which the probability for the cat to be alive (or dead) is $1/2+\sqrt 2/4\approx 0.854$

quant-ph↗

arXiv2003

Fermi-Pasta-Ulam $β$ lattice: Peierls equation and anomalous heat conductivity

The Peierls equation is considered for the Fermi-Pasta-Ulam $β$ lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal mode energy as a function of wave vector $k$ is estimated to be proportional to $k^{5/3}$. This leads to the $t^{-3/5}$ long time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained though the mode coupling theory our estimations give the same $k$ dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam $β$ lattice may lead to finite heat conductivity in this model.

cond-mat.stat-mech↗

arXiv2003

Damped harmonic oscillator: pure states of the bath and exact master equations

Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes - grand canonical ensemble, number states and coherent states. It is shown that for a wide class of number states the behavior of the oscillator is similar to the case of the equilibrium bath. If the bath modes are initially in coherent states, then the variances of the oscillator coordinate and momentum, as well as its entanglement to the bath, asymptotically approach the same values as for the oscillator at zero temperature and the average coordinate and momentum show a Brownian-like behavior. We derive an exact master equation for the characteristic function of the oscillator valid for arbitrary factorized initial conditions. In the case of the equilibrium bath this equation reduces to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it leads to an exact stochastic master equation with a multiplicative noise.

quant-ph↗