41 research outputs found
The EPR experiment in the energy-based stochastic reduction framework
We consider the EPR experiment in the energy-based stochastic reduction
framework. A gedanken set up is constructed to model the interaction of the
particles with the measurement devices. The evolution of particles' density
matrix is analytically derived. We compute the dependence of the
disentanglement rate on the parameters of the model, and study the dependence
of the outcome probabilities on the noise trajectories. Finally, we argue that
these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure
Quasi-classical Molecular Dynamics Simulations of the Electron Gas: Dynamic properties
Results of quasi-classical molecular dynamics simulations of the quantum
electron gas are reported. Quantum effects corresponding to the Pauli and the
Heisenberg principle are modeled by an effective momentum-dependent
Hamiltonian. The velocity autocorrelation functions and the dynamic structure
factors have been computed. A comparison with theoretical predictions was
performed.Comment: 8 figure
Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests
We present a procedure to solve the inverse Ising problem, that is to find
the interactions between a set of binary variables from the measure of their
equilibrium correlations. The method consists in constructing and selecting
specific clusters of variables, based on their contributions to the
cross-entropy of the Ising model. Small contributions are discarded to avoid
overfitting and to make the computation tractable. The properties of the
cluster expansion and its performances on synthetic data are studied. To make
the implementation easier we give the pseudo-code of the algorithm.Comment: Paper submitted to Journal of Statistical Physic
Renormalized kinetic theory of classical fluids in and out of equilibrium
We present a theory for the construction of renormalized kinetic equations to
describe the dynamics of classical systems of particles in or out of
equilibrium. A closed, self-consistent set of evolution equations is derived
for the single-particle phase-space distribution function , the correlation
function , the retarded and advanced density response
functions to an external potential , and
the associated memory functions . The basis of the theory is an
effective action functional of external potentials that
contains all information about the dynamical properties of the system. In
particular, its functional derivatives generate successively the
single-particle phase-space density and all the correlation and density
response functions, which are coupled through an infinite hierarchy of
evolution equations. Traditional renormalization techniques are then used to
perform the closure of the hierarchy through memory functions. The latter
satisfy functional equations that can be used to devise systematic
approximations. The present formulation can be equally regarded as (i) a
generalization to dynamical problems of the density functional theory of fluids
in equilibrium and (ii) as the classical mechanical counterpart of the theory
of non-equilibrium Green's functions in quantum field theory. It unifies and
encompasses previous results for classical Hamiltonian systems with any initial
conditions. For equilibrium states, the theory reduces to the equilibrium
memory function approach. For non-equilibrium fluids, popular closures (e.g.
Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the
correspondence with the seminal approaches of Martin-Siggia-Rose and of
Rose.and we discuss the correspondence with the seminal approaches of
Martin-Siggia-Rose and of Rose.Comment: 63 pages, 10 figure
Dislocation-Mediated Melting: The One-Component Plasma Limit
The melting parameter of a classical one-component plasma is
estimated using a relation between melting temperature, density, shear modulus,
and crystal coordination number that follows from our model of
dislocation-mediated melting. We obtain in good agreement
with the results of numerous Monte-Carlo calculations.Comment: 8 pages, LaTe
More is the Same; Phase Transitions and Mean Field Theories
This paper looks at the early theory of phase transitions. It considers a
group of related concepts derived from condensed matter and statistical
physics. The key technical ideas here go under the names of "singularity",
"order parameter", "mean field theory", and "variational method".
In a less technical vein, the question here is how can matter, ordinary
matter, support a diversity of forms. We see this diversity each time we
observe ice in contact with liquid water or see water vapor, "steam", come up
from a pot of heated water. Different phases can be qualitatively different in
that walking on ice is well within human capacity, but walking on liquid water
is proverbially forbidden to ordinary humans. These differences have been
apparent to humankind for millennia, but only brought within the domain of
scientific understanding since the 1880s.
A phase transition is a change from one behavior to another. A first order
phase transition involves a discontinuous jump in a some statistical variable
of the system. The discontinuous property is called the order parameter. Each
phase transitions has its own order parameter that range over a tremendous
variety of physical properties. These properties include the density of a
liquid gas transition, the magnetization in a ferromagnet, the size of a
connected cluster in a percolation transition, and a condensate wave function
in a superfluid or superconductor. A continuous transition occurs when that
jump approaches zero. This note is about statistical mechanics and the
development of mean field theory as a basis for a partial understanding of this
phenomenon.Comment: 25 pages, 6 figure
Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
When Lenz proposed a simple model for phase transitions in magnetism, he
couldn't have imagined that the "Ising model" was to become a jewel in field of
equilibrium statistical mechanics. Its role spans the spectrum, from a good
pedagogical example to a universality class in critical phenomena. A quarter
century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing
a seemingly trivial modification to the Ising lattice gas, they took it into
the vast realms of non-equilibrium statistical mechanics. An abundant variety
of unexpected behavior emerged and caught many of us by surprise. We present a
brief review of some of the new insights garnered and some of the outstanding
puzzles, as well as speculate on the model's role in the future of
non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting,
Rutgers, NJ (December, 2008
Physically Similar Systems - A History of the Concept
PreprintThe concept of similar systems arose in physics, and appears to have originated with Newton in the
seventeenth century. This chapter provides a critical history of the concept of physically similar
systems, the twentieth century concept into which it developed. The concept was used in the
nineteenth century in various fields of engineering (Froude, Bertrand, Reech), theoretical physics (van
der Waals, Onnes, Lorentz, Maxwell, Boltzmann) and theoretical and experimental hydrodynamics
(Stokes, Helmholtz, Reynolds, Prandtl, Rayleigh). In 1914, it was articulated in terms of ideas
developed in the eighteenth century and used in nineteenth century mathematics and mechanics:
equations, functions and dimensional analysis. The terminology physically similar systems was
proposed for this new characterization of similar systems by the physicist Edgar Buckingham.
Related work by Vaschy, Bertrand, and Riabouchinsky had appeared by then. The concept is very
powerful in studying physical phenomena both theoretically and experimentally. As it is not currently
part of the core curricula of STEM disciplines or philosophy of science, it is not as well known as it
ought to be
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Equation of State of Classical Systems of Charged Particles
Recent developments in the classical theory of fully ionized gases and strong electrolyte solutions are reviewed, and are used to discuss the equation of state at high temperatures and low densities. The pressure is calculated using the ring-integral approximation, and quantitative estimates of higher correction terms are given. The effect of short range repulsive forces is shown by comparing the results with two kinds of potential functions hard spheres of diameter a, and soft'' spheres for which the short range potential cancels the Coulomb potential at the origin, and decreases exponentially with distance. It is found that the use of either type of potential extends the range of validity of the ring-integral approximation to considerably higher densities and lower temperatures. Since there is little difference in the results for the hard spheres and the soft spheres in this range, the latter system is investigated more extensively since it is more, easily handled by analytical methods. The expressions derived for the free energy of a system of charged particles can also be used in ionization equilibrium calculations, and the effect of electrostatic interactions on the equilibrium concentrations of various kinds of ions is indicated. 60 references. (auth