arXiv subjects

Ph. A. Martin

Publications and source records attributed to Ph. A. Martin.

15 recordsLinked to original sources

arXiv2009

Atom-wall dispersive forces: a microscopic approach

We present a study of atom-wall interactions in non-relativistic quantum electrodynamics by functional integral methods. The Feynman-Kac path integral representation is generalized to the case when the particle interacts with a radiation field, providing an additional effective potential that contains all the interactions induced by the field. We show how one can retrieve the standard van der Waals, Casimir-Polder and classical Lifshiftz forces in this formalism for an atom in its ground state. Moreover, when electrostatic interactions are screened in the medium, we find low temperature corrections that are not included in the Lifshitz theory of fluctuating forces and are opposite to them.

quant-ph↗

arXiv2007

Microscopic theory of the Casimir force at thermal equilibrium: large-separation asymptotics

We present an entirely microscopic calculation of the Casimir force $f(d)$ between two metallic plates in the limit of large separation $d$. The models of metals consist of mobile quantum charges in thermal equilibrium with the photon field at positive temperature $T$. Fluctuations of all degrees of freedom, matter and field, are treated according to the principles of quantum electrodynamics and statistical physics without recourse to approximations or intermediate assumptions. Our main result is the correctness of the asymptotic universal formula $ f(d) \sim -\frac{ζ(3) \kB T}{8πd^3}$, $d\to\infty$. This supports the fact that, in the framework of Lifshitz' theory of electromagnetic fluctuations, transverse electric modes do not contribute in this regime. Moreover the microscopic origin of universality is seen to rely on perfect screening sum rules that hold in great generality for conducting media.

quant-ph↗

arXiv2006

The Casimir Effect

After a review of the standard calculation of the Casimir force between two metallic plates at zero and non-zero temperatures, we present the study of microscopic models to determine the large-distance asymptotic force in the high-temperature regime. Casimir's conducting plates are modelized by plasmas of interacting charges at temperature T. The charges are either classical, or quantum-mechanical and coupled to a (classical) radiation field. In these models, the force obtained is twice weaker than that arising from standard treatments neglecting the microscopic charge fluctutations inside the bodies. The enforcement of inert boundary conditions on the field in the usual calculations turns out to be inadequate in this regime. Other aspects of dispersion forces are also reviewed. The status of (non-retarded) van der Waals-London forces in a dilute medium of non-zero temperature and density is investigated. In a proper scaling regime called the atomic limit (high dilution and low temperature), one is able to give the exact large-distance atomic correlations up to exponentially small terms as T->0. Retarded van der Waals forces and forces between dielectric bodies are also reviewed. Finally, the Casimir effect in critical phenomena is addressed by considering the free Bose gas. It is shown that the grand-canonical potential of the gas in a slab at the critical value of the chemical potential has finite size corrections of the standard Casimir type. They can be attributed to the existence of long-range order generated by gapless excitations in the phase with broken continuous symmetry.

cond-mat.stat-mech↗

arXiv2005

The Casimir force at high temperature

The standard expression of the high-temperature Casimir force between perfect conductors is obtained by imposing macroscopic boundary conditions on the electromagnetic field at metallic interfaces. This force is twice larger than that computed in microscopic classical models allowing for charge fluctuations inside the conductors. We present a direct computation of the force between two quantum plasma slabs in the framework of non relativistic quantum electrodynamics including quantum and thermal fluctuations of both matter and field. In the semi-classical regime, the asymptotic force at large slab separation is identical to that found in the above purely classical models, which is therefore the right result. We conclude that when calculating the Casimir force at non-zero temperature, fluctuations inside the conductors can not be ignored.

cond-mat.stat-mech↗

arXiv2004

The Bose gas beyond mean field

We study a homogeneous Bose gas with purely repulsive forces. Using the Kac scaling of the binary potential we derive analytically the form of the thermodynamic functions of the gas for small but finite values of the scaling parameter in the low density regime. In this way we determine dominant corrections to the mean-field theory. It turns out that repulsive forces increase the pressure at fixed density and decrease the density at given chemical potential (the temperature is kept constant). They also flatten the Bose momentum distribution. However, the present analysis cannot be extended to the region where the mean-field theory predicts the appearence of condensate.

cond-mat.stat-mech↗

arXiv2004

Microscopic origin of universality in Casimir forces

The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance $d$ containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluids.

cond-mat.stat-mech↗

arXiv2003

Screened cluster expansions for partially ionized gases

We consider a partially ionized gas at thermal equilibrium, in the Saha regime. The system is described in terms of a quantum plasma of nuclei and electrons. In this framework, the Coulomb interaction is the source of a large variety of phenomena occuring at different scales: recombination, screening, diffraction, etc. In this paper, we derive a cluster expansion adequate for a coherent treatment of those phenomena. The expansion is obtained by combining the path integral representation of the quantum gas with familiar Mayer diagrammatics. In this formalism, graphs have a clear physical interpretation: vertices are associated with recombined chemical species, while bonds describe their mutual interactions. The diagrammatical rules account exactly for all effects in the medium. Applications to thermodynamics, van der Waals forces and dielectric versus conductive behaviour will be presented in forthcoming papers.

cond-mat.stat-mech↗

arXiv2003

Dielectric versus conductive behaviour in quantum gases: exact results for the hydrogen plasma

We study the electrical susceptibility of a hydrogen gas at equilibrium, partially ionized by thermal excitations. The gas is described as a quantum plasma of point protons and electrons, interacting via the Coulomb potential. Using the newly developped diagrammatical technique of screened cluster expansions, we calculate exactly the wavenumber-dependent susceptibility in the atomic limit, where most charges are bound into hydrogen atoms. A transition from conductive to dielectric behaviour occurs when the wave length is decreased well below the Debye screening length. The standard formula for the dielectric function of an ideal gas of hydrogen atoms is recovered in an appropriate scaling limit. The derivation treats all effects arising from the Coulomb interaction (screening, binding, polarization) in a fully coherent way, without intermediate approximation nor modelization.

cond-mat.stat-mech↗

arXiv1999

Ballistic aggregation: a solvable model of irreversible many particles dynamics

The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system of two coupled equations for a large class of initial conditions. The solution to these nonlinear equations is found by a direct construction of the relevant probability distributions in the limit of a continuous initial mass distribution. We show that those limiting distributions are identical to those of the statistics of shocks in the Burgers turbulence. The analysis relies on a mapping on a Brownian motion problem with parabolic constraints.

cond-mat.stat-mech↗

arXiv1999

Exact statistical properties of the Burgers equation

The one dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behavior of spatial correlations of the field is determined. Since higher order distributions factorize in terms of the one and two points functions, our analysis provides an explicit and complete statistical description of this problem.

cond-mat.stat-mech↗

arXiv1999

Coulomb systems at low density

Results on the correlations of low density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system -- Debye-Hückel screening -- is compared and contrasted with the quantum case where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye-Hückel screening is discussed.

cond-mat.stat-mech↗

arXiv1998

On edge states in semi-infinite quantum Hall systems

We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total Hamiltonian necessarily has a continuous spectrum in some intervals in-between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak. The spatial decay of the impurity potential is not needed. In particular this proves the occurence of edge states in semi-infinite quantum Hall systems.

cond-mat.mes-hall↗

arXiv1998

Thermalization of a particle with dissipative collisions

One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a stationary Maxwellian velocity distribution, with an effective temperature smaller than $T$. This effective temperature is explicitly given in terms of the restitution parameter and the masses.

cond-mat.stat-mech↗

arXiv1998

Lorentz's model with dissipative collisions

Propagation of a particle accelerated by an external field through a scattering medium is studied within the generalized Lorentz model allowing inelastic collisions. Energy losses at collisions are proportional to $(1-α^{2})$, where $0\leα\le 1$ is the restitution coefficient. For $α=1$ (elastic collisions) there is no stationary state. It is proved in one dimension that when $α<1$ the stationary state exists . The corresponding velocity distribution changes from a highly asymmetric half-gaussian ($α=0$) to an asymptotically symmetric distribution $\sim {\rm exp}[-(1-α)v^{4}/2]$, for $α\to 1$. The identical scaling behavior in the limit of weak inelasticity is derived in three dimensions by a self-consistent perturbation analysis, in accordance with the behavior of rigorously evaluated moments. The dependence on the external field scales out in any dimension, predicting in particular the stationary current to be proportional to the square root of the external acceleration.

cond-mat.stat-mech↗

arXiv1998

Statistics of Mass Aggregation in a Large Self-Gravitating One-Dimensional Gas

We study at the microscopic level the dynamics of a one-dimensional gravitationally interacting sticky gas. Initially, N identical particles of mass m with uncorrelated, randomly distributed velocities fill homogeneously a finite region of space. It is proved that at a characteristic time a single macroscopic mass is formed with certainty, surrounded by a dust of non extensive fragments. In the continuum limit this corresponds to a single shock creating a singular mass density. The statistics of the remaining fragments obeys the Poisson law at all times following the shock. Numerical simulations indicate that up to the moment of macroscopic aggregation the system remains internally homogeneous. At the short time scale a rapid decrease in the kinetic energy is observed, accompanied by the formation of a number sqrt(N) of aggregates with masses sqrt(N).

cond-mat.stat-mech↗