arXiv subjects

András Csordás

Publications and source records attributed to András Csordás.

12 recordsLinked to original sources

arXiv2026

Beyond Gaussian Entanglement: Practical Criteria for Polynomially Excited Quantum States

Polynomial excitations consisting of creation and annihilation operators are studied. Subsystem entanglement is proven produced and preserved by such manipulations. NPT entanglement already present between any two subsystems of a general pure or mixed multipartite Gaussian state is preserved under all polynomial excitations. Nevertheless, these excitations can create NPT entanglement between initially separable subsystems, implying that the number of NPT entangled pairs cannot decrease. Polynomial excitations of a wide class of initially separable pure states are considered. For these states, the method reduces the infinite-dimensional positivity problem to a finite-dimensional one: after partial transposition, NPT entanglement is equivalent to a corresponding bilinear representation matrix not being positive semi-definite. Furthermore, using symplectic diagonalization and spectral decomposition, an explicit transformation is constructed between the Fock-space and position representations. It is applied to quadratic excitations of a three-mode mixed Gaussian state. The behavior of the NPT entanglement is tracked between subsystems as a function of a parameter $κ$, which tunes the non-locality of the excitation, and quantum negativity is evaluated. Under a chosen quadratic Hamiltonian, the resulting unitary time evolution maintains NPT entanglement for long intervals, interrupted only by short periods of PPT states. Finally, a closed analytical expression is derived for the covariance matrix of a general quadratic operator for an arbitrary number of degrees of freedom in phase space. Our framework directly connects mathematical foundations, theoretical modeling, and experimentally feasible implementations.

quant-ph↗

arXiv2026

An exact Markovian decoherence dynamics of two interacting harmonic oscillators coupled to a bosonic heat bath

We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz-Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system's entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.

quant-ph↗

arXiv2025

Effective eigenvalue approximation from moments for self-adjoint trace-class operators

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $Λ_n\subset \mathbb{R}$, and we show that it converges to the spectrum of $O$ in the Hausdorff metric under mild conditions. Our set $Λ_n$ only depends on the first $n$ moments of $O$. We show that it can be effectively calculated for physically relevant operators, and it approximates the spectrum well without diagonalization. We prove that using the above method we can converge to the minimal and maximal eigenvalues with super-exponential speed. We also construct monotone increasing lower bounds $q_n$ for the minimal eigenvalue (or decreasing upper bounds for the maximal eigenvalue). This sequence only depends on the moments of $O$ and a concrete upper estimate of its $1$-norm; we also demonstrate that $q_n$ can be effectively calculated for a large class of physically relevant operators. This rigorous lower bound $q_n$ tends to the minimal eigenvalue with super-exponential speed provided that $O$ is not positive semidefinite. As a by-product, we obtain computable upper bounds for the $1$-norm of $O$, too. Numerical examples demonstrate the relevance of our approximation in estimating entropy and negativity, which is useful, among others, in quantum optical and in open quantum system models. The results can be directly applicable to problems in quantum information, statistical mechanics, and quantum thermodynamics, where using traditional techniques based on diagonalization is impractical.

quant-ph↗

arXiv2024

Positivity and entanglement of polynomial Gaussian integral operators

Positivity preservation is an important issue in the dynamics of open quantum systems: positivity violations always mark the border of validity of the model. We investigate the positivity of self-adjoint polynomial Gaussian integral operators $\widehatκ_{PG}$, that is, the multivariable kernel $κ_{PG}$ is a product of a polynomial $P$ and a Gaussian kernel $κ_G$. These operators frequently appear in open quantum systems. We show that $\widehatκ_{PG}$ can be only positive if the Gaussian part is positive, which yields a strong and quite easy test for positivity. This has an important corollary for the bipartite entanglement of the density operators $\widehatκ_{PG}$: if the Gaussian density operator $\widehatκ_G$ fails the Peres-Horodecki criterion, then the corresponding polynomial Gaussian density operators $\widehatκ_{PG}$ also fail the criterion for all $P$, hence they are all entangled. We prove that polynomial Gaussian operators with polynomials of odd degree cannot be positive semidefinite. We introduce a new preorder $\preceq$ on Gaussian kernels such that if $κ_{G_0}\preceq κ_{G_1}$ then $\widehatκ_{PG_0}\geq 0$ implies $\widehatκ_{PG_1}\geq 0$ for all polynomials $P$. Therefore, deciding the positivity of a polynomial Gaussian operator determines the positivity of a lot of another polynomial Gaussian operators having the same polynomial factor, which might improve any given positivity test by carrying it out on a much larger set of operators. We will show an example that this really can make positivity tests much more sensitive and efficient. This preorder has implication for the entanglement problem, too.

quant-ph↗

arXiv2006

Rashba billiards

We study the energy levels of non-interacting electrons confined to move in two-dimensional billiard regions and having a spin-dependent dynamics due to a finite Rashba spin splitting. The Green's function for such Rashba billiards is constructed analytically and used to find the area and perimeter contributions to the density of states, as well as the smooth counting function. We show that, in contrast to systems with spin-rotational invariance, Rashba billiards always possess a negative energy spectrum. A semi-classical analysis is presented to interpret the singular behavior of the density of states at certain negative energies. Our detailed analysis of the spin structure of Rashba billiards reveals a finite out-of-plane spin projection for electron eigenstates.

cond-mat.mes-hall↗

arXiv2004

Electronic and spin properties of Rashba billiards

Ballistic electrons confined to a billiard and subject to spin--orbit coupling of the Rashba type are investigated, using both approximate semiclassical and exact quantum--mechanical methods. We focus on the low--energy part of the spectrum that has negative eigenvalues. When the spin precession length is smaller than the radius of the billiard, the low--lying energy eigenvalues turn out to be well described semiclassically. Corresponding eigenspinors are found to have a finite spin polarization in the direction perpendicular to the billiard plane.

cond-mat.mes-hall↗

arXiv2000

Finite temperature hydrodynamic modes of trapped quantum gases

The hydrodynamic equations of an ideal fluid formed by a dilute quantum gas in a parabolic trapping potential are studied analytically and numerically. Due to the appearance of internal modes in the fluid stratified by the trapping potential, the spectrum of low-lying modes is found to be dense in the high-temperature limit, with an infinitely degenerate set of zero-frequency modes. The spectrum for Bose-fluids and Fermi-fluids is obtained and discussed.

cond-mat↗

arXiv2000

Collective excitations of degenerate Fermi gases in anisotropic parabolic traps

The hydrodynamic low-frequency oscillations of highly degenerate Fermi gases trapped in anisotropic harmonic potentials are investigated. Despite the lack of an obvious spatial symmetry the wave-equation turns out to be separable in elliptical coordinates, similar to a corresponding result established earlier for Bose-condensates. This result is used to give the analytical solution of the anisotropic wave equation for the hydrodynamic modes.

cond-mat.soft↗

arXiv1998

Collective excitations in Bose-Einstein condensates in triaxially anisotropic parabolic traps

The wave equation of low-frequency density waves in Bose-Einstein condensates at vanishing temperature in arbitrarily anisotropic harmonic traps is separable in elliptic coordinates, provided the condensate can be treated in the Thomas-Fermi approximation. We present a complete solution of the mode functions, which are polynomials of finite order, and their eigenfrequencies which are characterized by three integer quantum numbers.

cond-mat↗

arXiv1997

Quasi-particle excitations and dynamical structure function of trapped Bose-condensates in the WKB approximation

The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light-scattering.

cond-mat↗

arXiv1997

Classical quasi-particle dynamics in trapped Bose condensates

The dynamics of quasi-particles in repulsive Bose condensates in a harmonic trap is studied in the classical limit. In isotropic traps the classical motion is integrable and separable in spherical coordinates. In anisotropic traps the classical dynamics is found, in general, to be nonintegrable. For quasi-particle energies E much smaller than thechemical potential, besides the conserved quasi-particle energy, we identify two additional nearly conserved phase-space functions. These render the dynamics inside the condensate (collective dynamics) integrable asymptotically for E/chemical potential very small. However, there coexists at the same energy a dynamics confined to the surface of the condensate, which is governed by a classical Hartree-Fock Hamiltonian. We find that also this dynamics becomes integrable for E/chemical potential very small, because of the appearance of an adiabatic invariant. For E/chemical potential of order 1 a large portion of the phase-space supports chaotic motion, both, for the Bogoliubov Hamiltonian and its Hartree-Fock approximant. To exemplify this we exhibit Poincaré surface of sections for harmonic traps with the cylindrical symmetry and anisotropy found in TOP traps. For E/chemical potential very large the dynamics is again governed by the Hartree-Fock Hamiltonian. In the case with cylindrical symmetry it becomes quasi-integrable because the remaining small chaotic components in phase space are tightly confined by tori.

cond-mat↗

arXiv1997

Hydrodynamic excitations of Bose condensates in anisotropic traps

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.

cond-mat↗