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Martin Wilkens

Publications and source records attributed to Martin Wilkens.

14 recordsLinked to original sources
arXiv2022

Haake-Lewenstein-Wilkens approach to spin-glasses revisited

We revisit the Haake-Lewenstein-Wilkens (HLW) approach to Edwards-Anderson (EA) model of Ising spin glass [Phys. Rev. Lett. 55, 2606 (1985)]. This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, qEA. We use saddle point/steepest descent method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that qEA >0 at 0 <T <Tc in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts spin glass order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; ii) There is (no) spin glass transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak.

cond-mat.dis-nn↗
arXiv2016

Gravitational properties of light - The emission of counter-propagating laser pulses from an atom

The gravitational field of a laser pulse, although not detectable at the moment, comes with a peculiar feature which continues to attract attention; cause and effect propagate with the same speed, that of light. A particular result of this feature is that the gravitational field of an emitted laser pulse and the gravitational effect of the emitter's energy-momentum change are intimately entangled. In this article, a specific example of an emission process is considered - an atom, modeled as a point mass, emits two counter-propagating pulses. The corresponding curvature and the effect on massive and massless test particles is discussed. A comparison is made with the metric corresponding to a spherically symmetric massive object that isotropically emits radiation - the Vaidya metric.

gr-qc↗
arXiv2016

The effect of polarization entanglement in photon-photon scattering

It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced, general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in Quantum Electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces.

quant-ph↗
arXiv2016

The effect of entanglement in gravitational photon-photon scattering

The differential cross section for gravitational photon-photon scattering calculated in Perturbative Quantum Gravity is shown to depend on the degree of polarization entanglement of the two photons. The interaction between photons in the symmetric Bell state is stronger than between not entangled photons. In contrast, the interaction between photons in the anti-symmetric Bell state is weaker than between not entangled photons. The results are interpreted in terms of quantum interference, and it is shown how they fit into the idea of distance-dependent forces.

quant-ph↗
arXiv2015

Gravitational properties of light - The gravitational field of a laser pulse

The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are associated with the emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.

quant-ph↗
arXiv2003

Ground-state properties of trapped Bose-Fermi mixtures: role of exchange-correlation

We introduce Density Functional Theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local density approximation. We solve numerically the Kohn-Sham system and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange--correlation is discussed by comparison with current experiments; in particular, we investigate the effect of of the repulsive potential energy contribution due to exchange--correlation on the stability of the mixture against collapse.

cond-mat↗
arXiv2002

Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction

We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a trans-disciplinary perspective (astrophysics, nuclear physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special emphasis on Bose-Einstein condensates.

cond-mat.stat-mech↗
arXiv2002

Quantum field theory of dilute homogeneous Bose-Fermi-mixtures at zero temperature: general formalismand beyond mean-field corrections

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean-field stems from the boson-fermion interaction and is proportional to $a_{\scriptsize BF}k_{\scriptsize F}$. The total ground-state energy-density reads $E/V = ε_{\scriptsize F} + ε_{\scriptsize B} + (2π\hbar^{2}a_{\rm BF}n_{\scriptsize B}n_{\scriptsize F}/m) [1 + a_{\scriptsize BF}k_{\scriptsize F}f(δ)/π]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(δ)$ is a known function of $δ= (m_{\scriptsize B} - m_{\scriptsize F})/(m_{\scriptsize B} + m_{\scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.

cond-mat↗
arXiv2001

Phonon spectrum and dynamical stability of a quantum degenerate Bose-Fermi mixture

We calculate the phonon excitation spectrum in a zero-temperature boson-fermion mixture. We show how the sound velocity changes due to the boson-fermion interaction and we determine the dynamical stability regime of a homogeneous mixture. We identify a resonant phonon-exchange interaction between the fermions as the physical mechanism leading to the instability.

cond-mat.soft↗
arXiv2000

Dependence of the BEC transition temperature on interaction strength: a perturbative analysis

We compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93 aρ^{1/3}$, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and $ρ$ is the particle number density.

cond-mat.stat-mech↗
arXiv1999

Loss and heating of particles in small and noisy traps

We derive the life time and loss rate for a trapped particle that is coupled to fluctuating fields in the vicinity of a room-temperature metallic and/or dielectric surface. Our results indicate a clear predominance of near field effects over ordinary blackbody radiation. We develop a theoretical framework for both charged and neutral particles with and without spin. Loss processes that are due to a transition to an untrapped internal state are included.

quant-ph↗
arXiv1999

Thermodynamic identities and particle number fluctuations in weakly interacting Bose--Einstein condensates

We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of {\it auxiliary partition functions} for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, at variance with the anomalous scaling behavior V^{4/3} of the fluctuations in the ideal Bose gas.

cond-mat↗
arXiv1999

Heating of trapped atoms near thermal surfaces

We study the electromagnetic coupling and concomitant heating of a particle in a miniaturized trap close to a solid surface. Two dominant heating mechanisms are identified: proximity fields generated by thermally excited currents in the absorbing solid and time-dependent image potentials due to elastic surface distortions (Rayleigh phonons). Estimates for the lifetime of the trap ground state are given. Ions are particularly sensitive to electric proximity fields: for a silver substrate, we find a lifetime below one second at distances closer than some ten micrometer to the surface. Neutral atoms may approach the surface more closely: if they have a magnetic moment, a minimum distance of one micrometer is estimated in tight traps, the heat being transferred via magnetic proximity fields. For spinless atoms, heat is transferred by inelastic scattering of virtual photons off surface phonons. The corresponding lifetime, however, is estimated to be extremely long compared to the timescale of typical experiments.

quant-ph↗