arXiv subjects

A. Csordás

Publications and source records attributed to A. Csordás.

10 recordsLinked to original sources

arXiv2023

Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check

We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.

quant-ph↗

arXiv2023

Newton's identities and positivity of trace class integral operators

We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for a trace class integral operator to be positive semidefinite, which is an important cornerstone for quantum theory in phase-space representation. We also present a new, efficiently computable algorithm based on Newton's identities. Our test of positivity is much more sensitive than the ones given by the linear entropy and Robertson-Schrödinger's uncertainty relations; our first condition is equivalent to the non-negativity of the linear entropy.

quant-ph↗

arXiv2020

Range of applicability of the Hu-Paz-Zhang master equation

We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small-times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.

quant-ph↗

arXiv2015

Protected edge states in silicene antidots and dots in magnetic field

Silicene systems, due to the buckled structure of the lattice, manifest remarkable intrinsic spin-orbit interaction triggering a topological phase transition in the low-energy regime. Thus, we found that protected edge states are present in silicene antidots and dots, being polarized in valley-spin pairs. We have also studied the effect of the lattice termination on the properties of the single electron energy levels and electron density distribution of silicene antidots and dots situated in a perpendicular magnetic field. Our calculations confirmed that the topological edge states are propagating over the perimeter of the antidot/dot for both ideal or realistic edge termination containing roughness on the atomic length scale. The valley polarization and the slope of the energy line as a function of the magnetic field is, however, reduced when the antidot or dot has a rough edge.

cond-mat.mes-hall↗

arXiv2014

Emergence of bound states in ballistic magnetotransport of graphene antidots

An experimental method for detection of bound states around an antidot formed from a hole in a graphene sheet is proposed by measuring the ballistic two terminal conductances. In particularly, we consider the effect of bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states. In addition, we develop a new numerical method in which the computational effort is proportional to the linear dimensions, instead of the area of the scattering region beeing typical for the existing numerical recursive Green's function method.

cond-mat.mes-hall↗

arXiv2012

Calculation of the even-odd energy difference in superfluid Fermi systems using the pseudopotential theory

The pseudopotential theory is extended to the Bogoliubov-de Gennes equations to determine the excess energy when one atom is added to the trapped superfluid Fermi system with even number of atoms. Particular attention is paid to systems being at the Feshbach resonance point. The results for relatively small particle numbers are in harmony with the Monte-Carlo calculations, but are also relevant for systems with larger particle numbers. Concerning the additional one quasiparticle state we define and determine two new universal numbers to characterize its widths.

cond-mat.quant-gas↗

arXiv2007

Role of the trigonal warping on the minimal conductivity of bilayer graphene

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is three times as large as that without trigonal warping, and six times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.

cond-mat.mes-hall↗

arXiv1999

Shifts and widths of collective excitations in trapped Bose gases by the dielectric formalism

We present predictions for the temperature dependent shifts and damping rates. They are obtained by applying the dielectric formalism to a simple model of a trapped Bose gas. Within the framework of the model we use lowest order perturbation theory to determine the first order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured at JILA are found for the m=2 mode, while we find disagreements in the shifts for m=0. The latter point to the necessity of a non-perturbative treatment for an explanation of the temperature-dependence of the m=0 shifts.

cond-mat↗

arXiv1998

Finite temperature excitations of Bose gases in anisotropic traps

The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation (HFB-Popov) are used for our calculations. The new feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero-temperature condensate (EZC) approximation which involves a much simpler model.

cond-mat↗

arXiv1997

Transition from Poissonian to GOE level statistics in a modified Artin's billiard

One wall of Artin's billiard on the Poincaré half plane is replaced by a one-parameter ($c_p$) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuousand gradual transition from the Poisson like to GOE level statistics due to the small perturbations breaking the symmetry responsible for the 'arithmetic chaos' at $c_p=1$ is studied. Another GOE $\rightrrow$ Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in boh cases. The study supports the existence of a scaling region around $c_p=1$. A finite size scaling relation for the Brody-parameter as a function of $1-c_p$ and the number of levels considered can be established.

chao-dyn↗