arXiv subjects

Yamen Hamdouni

Publications and source records attributed to Yamen Hamdouni.

14 recordsLinked to original sources

arXiv2024

Diffusion coefficients preserving long-time correlations: Consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system

We analytically derive the diffusion coefficients that drive a system of $N$ coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients, provided that the physical constraints are fulfilled. We also investigate the entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down the entanglement sudden death, and for initially separable states, entanglement generation may occur.

quant-ph↗

arXiv2024

Exact lower bound of the uncertainty principle product for the harmonic oscillator with position-momentum coupling

We show that the uncertainty principle product for the position and momentum operators for a system described by the Hamiltonian $ \hat H= \frac{\hat{p}^2}{2m} +\frac{1}{2} m ω^2 \hat{x}^2+\fracμ{2}(\hat x \hat p+ \hat p \hat x)$ where $μ<ω$ reads $Δx Δp\ge\frac{\hbar ω}{2\sqrt{ω^2-μ^2}}$. All the values bellow this lower bound are thus quantum-mechanically forbidden. We construct the annihilation and creation operators for this system and we calculate the expectation values of the operators $\hat p$ and $\hat x$ with respect to the corresponding coherent states.

quant-ph↗

arXiv2023

Quantum mean-field treatment of the dynamics of a two-level atom in a simple cubic lattice

The mean field approximation is used to investigate the general features of the dynamics of a two-level atom in a ferromagnetic lattice close to the Curie temperature. Various analytical and numerical results are obtained. We first linearize the lattice Hamiltonian, and we derive the self-consistency equation for the order parameter of the phase transition for arbitrary direction of the magnetic field. The reduced dynamics is deduced by tracing out the degrees of freedom of the lattice, which results in the reduction of the dynamics to that of an atom in an effective spin bath whose size is equal to the size of a unit cell of the lattice. It is found that the dephasing and the excited state occupation probability may be enhanced by applying the magnetic field along some specific directions. The dependence on the change of the temperature and the magnitude of spin is also investigated. It turns out that the increase of thermal fluctuations may reduce the occupation probability of the excited state. The entanglement of two such atoms that occupy non-adjacent cells is studied and its variation in time is found to be not much sensitive to the direction of the magnetic field. Entanglement sudden death and revival is shown to occur close to the critical temperature.

quant-ph↗

arXiv2023

The internal energy, the magnetization and the specific heat of the Heisenberg XX chain at low temperatures

We derive power series expansions for the magnetization, the internal energy, and the specific heat of the Heisenberg XX chain that are valid at low temperatures. The coefficients of the series obtained depend logarithmically on the fugacity. It is shown that depending on whether the magnetic field exceeds or not the critical point, the effects of either the coupling of the spins and the magnetic field can have different characters, as indicated by the different power laws established.

cond-mat.stat-mech↗

arXiv2022

Aspects of the decoherence in high spin environments: Breakdown of the mean-field approximation

The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-$\frac{1}{2}$ particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg $XY$ and Ising interactions. It is shown that while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg $XY$ interactions. In the case of a transverse Ising model, we find that the mean field approximation breaks down for high values of the spin.

quant-ph↗

arXiv2021

Quantum master equation approach to heat transport in dielectrics and semiconductors

We report on the derivation of the heat transport equation for nonmetals using a quantum Markovian master equation in Lindblad form. We first establish the equations of motion describing the time variation of the on-site energy of atoms in a one dimensional periodic chain that is coupled to a heat reservoir. In the continuum limit, the Fourier law of heat conduction naturally emerges, and the heat conductivity is explicitly obtained. It is found that the effect of the heat reservoir on the lattice is described by a heat source density that depends on the diffusion coefficients of the atoms. We show that the Markovian dynamics is equivalent to the long wavelength approximation for phonons, which is typical for the case of elastic solids. The high temperature limit is shown to reproduce the classical heat conduction equation.

quant-ph↗

arXiv2021

Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice

The decay rate of an interstitial two-level spin impurity, located in the center of a unit cell of an anisotropic ferromagnetic lattice subjected to an external magnetic field is derived. The impurity is coupled to nearest-neighbor spins through Heisenberg $XY$ interaction. By mapping the lattice spin operators using the Holstein-Primakoff transformation, we establish the similarity with the Fano-Anderson model at low temperatures, and we calculate the retarded Green's function in one and two dimensions analytically for arbitrary coupling strength. It is shown that the reduced density matrix of the impurity satisfies an exact master equation in Lindblad form, from which the decay rate and the Lamb shift are deduced. The evolution in time of the latter together with the excited state occupation probability is investigated and its dependence on the applied magnetic field is discussed. It is found that there exists a critical resonance-like value of the magnetic field around which the behavior of the decay rate and the density matrix changes drastically. The Markovian decay law, as given by the Fermi golden rule, does not hold in the weak-coupling regime unless the magnetic field is weak, typically less than the critical value. The weak-coupling regime is further treated perturbatively up to second order, and the obtained results are compared with the exact solution. We also discuss the Zeno regime of the dynamics, where it is shown that at short times, the effective decay rate is twice as small as the exact decay rate, and that when the impurity energy lies outside the lattice continuum, the measurement speeds up the decay of the survival probability.

quant-ph↗

arXiv2018

Random spin distributions and the diffusion equation

We show that the probability distribution corresponding to a fully random tracial state of a system of spin-S particles satisfies a diffusion-like equation. The diffusion coefficient turns out to be equal to $S(S+1)/6$, where $S$ is the magnitude of the spin of each particle. We also present a bosonization scheme for the lowering and raising total spin operators.

quant-ph↗

arXiv2016

Notes on the phase space formulation of the propagator of Hamiltonians with spatially-dependent kinetic energy

These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with arbitrary ordering ambiguity parameters, and a simple scheme to convert the problem to a constant-mass motion is presented. The motion in curved spaces is treated along the same lines, where a phase space formulation is used to derive the propagator for arbitrary discretization choices.

quant-ph↗

arXiv2015

A nontrivial bosonic representation of large spin systems at high temperatures

We report on a nontrivial bosonization scheme for spin operators. It is shown that in the large $N$ limit, at infinite temperature, the operators $\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$ behave like the creation and annihilation operators, $a^†$ and $a$, corresponding to a harmonic oscillator in thermal equilibrium, whose temperature and frequency are related by $\hbarω/k_B T=\ln 3$. The $z$ component is found to be equivalent to the position variable of another harmonic oscillator occupying its ground Gaussian state at zero temperature. The obtained results are applied to the Heisenberg XY Hamiltonian at finite temperature.

quant-ph↗

arXiv2011

Motion of position-dependent mass as a damping-antidamping process: Application to the Fermi gas and to the Morse potential

The object of this paper is to investigate, classically and quantum mechanically, the relation existing between the position-dependent effective mass and damping-antidamping dynamics. The quantization of the equations of motion is carried out using the geometric interpretation of the motion, and we compare it with the one based on the ordering ambiguity scheme. Furthermore, we apply the obtained results to a Fermi gas of damped-antidamped particles, and we solve the Schrödinger equation for an exponentially increasing (decreasing) mass in the presence of the Morse potential.

quant-ph↗

arXiv2010

On quantum mechanical transport coefficients in nonequilibrium nuclear processes with application to heavy-ion collisions

The elements of the quantum mechanical diffusion matrix, leading to a Gibbs equilibrium state for a set of $N$ coupled quantum harmonic oscillators are derived within Lindblad's axiomatic approach. Consequences of the fundamental constraints on the quantum friction coefficients are discussed. We derive the equations of motion for the expectation values and variances, and we solve them analytically. We apply our results to the description of the charge and mass asymmetry coordinates in heavy-ion collisions, and we investigate the effect of dissipation on tunneling in sub-barrier processes.

quant-ph↗

arXiv2008

Exactly solvable model for the dynamics of two spin-1/2 particles embedded in separate spin star environments

Exact analytical results for the dynamics of two interacting qubits each of which is embedded in its own spin star bath are presented. The time evolution of the concurrence and the purity of the two-qubit system is investigated for finite and infinite numbers of environmental spins. The effect of qubit-qubit interactions on the steady state of the central system is investigated

quant-ph↗

arXiv2008

On the partial trace over collective spin-degrees of freedom

We derive analytical properties for the degeneracy $ν(N,j)$ occurring in the decomposition $\bigoplus\limits_{j}^\frac{N}{2}ν(N,j)\mathbb C^{2j+1}$ of the state space $\mathbb C^{2\otimes N}$. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.

quant-ph↗