2,963 research outputs found
Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas
We analyze the extrapolation to the thermodynamic limit of Fermi liquid
properties of the homogeneous electron gas in two and three dimensions. Using
field theory, we explicitly calculate finite-size effects of the total energy,
the renormalization factor, and the effective mass at the Fermi surface within
the random phase approximation (RPA) and discuss the validity for general
metallic systems.Comment: 6 page
Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions
Several authors have considered the possibility of a generalized
Bose-Einstein condensation (BEC) in which a band of low states is occupied so
that the total occupation number is macroscopic, even if the occupation number
of each state is not extensive. The Hohenberg theorem (HT) states that there is
no BEC into a single state in 2D; we consider its validity for the case of a
generalized condensation and find that, under certain conditions, the HT does
not forbid a BEC in 2D. We discuss whether this situation actually occurs in
any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys.,
Quantum Fluids and Solids Conference QFS200
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
Many-body wavefunctions for normal liquid He
We present new trial wave-functions which include 3-body correlations into
the backflow coordinates and a 4-body symmetric potential. We show that our
wavefunctions lower the energy enough to stabilize the ground state energies of
normal liquid He in the unpolarized state at all pressures in agreement
with experiment; however, quantitative discrepancies remain. Further, we
include strong spin coupling into the Fermi liquid by adapting pairing wave
functions. We demonstrate a new, numerically stable method to evaluate pairing
functions which is also useful for Path Integrals calculations at low, but
non-zero temperatures.Comment: 5 page
A multi-paradigm language for reactive synthesis
This paper proposes a language for describing reactive synthesis problems
that integrates imperative and declarative elements. The semantics is defined
in terms of two-player turn-based infinite games with full information.
Currently, synthesis tools accept linear temporal logic (LTL) as input, but
this description is less structured and does not facilitate the expression of
sequential constraints. This motivates the use of a structured programming
language to specify synthesis problems. Transition systems and guarded commands
serve as imperative constructs, expressed in a syntax based on that of the
modeling language Promela. The syntax allows defining which player controls
data and control flow, and separating a program into assumptions and
guarantees. These notions are necessary for input to game solvers. The
integration of imperative and declarative paradigms allows using the paradigm
that is most appropriate for expressing each requirement. The declarative part
is expressed in the LTL fragment of generalized reactivity(1), which admits
efficient synthesis algorithms, extended with past LTL. The implementation
translates Promela to input for the Slugs synthesizer and is written in Python.
The AMBA AHB bus case study is revisited and synthesized efficiently,
identifying the need to reorder binary decision diagrams during strategy
construction, in order to prevent the exponential blowup observed in previous
work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
Shaping an ultracold atomic soliton in a travelling wave laser beam
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave
may form a many-atom soliton.This is disturbed by a homogeneous force field,
for example by the inevitable gravitation. The wave packet is accelerated and
therefore the laser frequency appears to be chirped in the rest frame of the
atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a
time dependent nonlinearity coefficient which amounts to a damping or
antidamping, respectively. The accelerated packet solution remains a soliton
which changes its shape adiabatically. Similarly, an active shaping can be
obtained in the force-free case by chirping the laser frequency thus
representing a way of coherent control of the soliton form. The experimental
consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let
- …