22,465 research outputs found
Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles
The purpose of this article is to discuss cluster expansions in dense quantum
systems as well as their interconnection with exchange cycles. We show in
general how the Ursell operators of order 3 or more contribute to an
exponential which corresponds to a mean-field energy involving the second
operator U2, instead of the potential itself as usual. In a first part, we
consider classical statistical mechanics and recall the relation between the
reducible part of the classical cluster integrals and the mean-field; we
introduce an alternative method to obtain the linear density contribution to
the mean-field, which is based on the notion of tree-diagrams and provides a
preview of the subsequent quantum calculations. We then proceed to study
quantum particles with Boltzmann statistics (distinguishable particles) and
show that each Ursell operator Un with n greater or equal to 3 contains a
``tree-reducible part'', which groups naturally with U2 through a linear chain
of binary interactions; this part contributes to the associated mean-field
experienced by particles in the fluid. The irreducible part, on the other hand,
corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra
holds in the case of Fermi or Bose particles, and discuss physically the role
of the exchange cycles, combined with interactions. Bose condensed systems are
not considered at this stage. The similarities and differences between
Boltzmann and quantum statistics are illustrated by this approach, in contrast
with field theoretical or Green's functions methods, which do not allow a
separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure
Landau levels, response functions and magnetic oscillations from a generalized Onsager relation
A generalized semiclassical quantization condition for cyclotron orbits was
recently proposed by Gao and Niu \cite{Gao}, that goes beyond the Onsager
relation \cite{Onsager}. In addition to the integrated density of states, it
formally involves magnetic response functions of all orders in the magnetic
field. In particular, up to second order, it requires the knowledge of the
spontaneous magnetization and the magnetic susceptibility, as was early
anticipated by Roth \cite{Roth}. We study three applications of this relation
focusing on two-dimensional electrons. First, we obtain magnetic response
functions from Landau levels. Second we obtain Landau levels from response
functions. Third we study magnetic oscillations in metals and propose a proper
way to analyze Landau plots (i.e. the oscillation index as a function of
the inverse magnetic field ) in order to extract quantities such as a
zero-field phase-shift. Whereas the frequency of -oscillations depends on
the zero-field energy spectrum, the zero-field phase-shift depends on the
geometry of the cell-periodic Bloch states via two contributions: the Berry
phase and the average orbital magnetic moment on the Fermi surface. We also
quantify deviations from linearity in Landau plots (i.e. aperiodic magnetic
oscillations), as recently measured in surface states of three-dimensional
topological insulators and emphasized by Wright and McKenzie \cite{Wright}.Comment: 31 pages, 8 figures; v2: SciPost style; v3: several references added,
small corrections, typos fixed; v4: abstract changed, generalized
quantization condition called Roth-Gao-Niu; v5: minor modifications, 2
references adde
Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory
The flow curves, viz. the curves of stationary stress under steady shearing,
are obtained close to the glass transition in dense colloidal dispersions using
asymptotic expansions in a schematic model of mode coupling theory. The shear
thinning of the viscosity in fluid states and the yielding of glassy states is
discussed. At the transition between fluid and shear-molten glass, simple and
generalized Herschel-Bulkley laws are derived with power law exponents that can
be computed for different particle interactions from the equilibrium structure
factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted
Large amplitude spin waves in ultra-cold gases
We discuss the theory of spin waves in non-degenerate ultra-cold gases, and
compare various methods which can be used to obtain appropriate kinetic
equations. We then study non-hydrodynamic situations, where the amplitude of
spin waves is sufficiently large to bring the system far from local
equilibrium. In the first part of the article, we compare two general methods
which can be used to derive a kinetic equation for a dilute gas of atoms
(bosons or fermions) with two internal states (treated as a pseudo-spin 1/2).
The collisional methods are in the spirit of Boltzmann's original derivation of
his kinetic equation where, at each point of space, the effects of all sorts of
possible binary collisions are added. We discuss two different versions of
collisional methods, the Yvon-Snider approach and the S matrix approach. The
second method uses the notion of mean field, which modifies the drift term of
the kinetic equation, in the line of the Landau theory of transport in quantum
liquids. For a dilute cold gas, it turns out that all these derivations lead to
the same drift terms in the transport equation, but differ in the precise
expression of the collision integral and in higher order gradient terms. In the
second part of the article, the kinetic equation is applied to spin waves in
trapped ultra-cold gases. Numerical simulations are used to illustrate the
strongly non-hydrodynamic character of the spin waves recently observed with
trapped Rb87 atoms. The decay of the phenomenon, which takes place when the
system relaxes back towards equilibrium, is also discussed, with a short
comment on decoherence.Comment: To appear in Eur. Phys. J.
Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
We analyze the slow, glassy structural relaxation as measured through
collective and tagged-particle density correlation functions obtained from
Brownian dynamics simulations for a polydisperse system of quasi-hard spheres
in the framework of the mode-coupling theory of the glass transition (MCT).
Asymptotic analyses show good agreement for the collective dynamics when
polydispersity effects are taken into account in a multi-component calculation,
but qualitative disagreement at small when the system is treated as
effectively monodisperse. The origin of the different small- behaviour is
attributed to the interplay between interdiffusion processes and structural
relaxation. Numerical solutions of the MCT equations are obtained taking
properly binned partial static structure factors from the simulations as input.
Accounting for a shift in the critical density, the collective density
correlation functions are well described by the theory at all densities
investigated in the simulations, with quantitative agreement best around the
maxima of the static structure factor, and worst around its minima. A
parameter-free comparison of the tagged-particle dynamics however reveals large
quantiative errors for small wave numbers that are connected to the well-known
decoupling of self-diffusion from structural relaxation and to dynamical
heterogeneities. While deviations from MCT behaviour are clearly seen in the
tagged-particle quantities for densities close to and on the liquid side of the
MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure
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