6,877 research outputs found
Is there Ornstein-Zernike equation in the canonical ensemble?
A general density-functional formalism using an extended variable-space is
presented for classical fluids in the canonical ensemble (CE). An exact
equation is derived that plays the role of the Ornstein-Zernike (OZ) equation
in the grand canonical ensemble (GCE). When applied to the ideal gas we obtain
the exact result for the total correlation function h_N. For a homogeneous
fluid with N particles the new equation only differs from OZ by 1/N and it
allows to obtain an approximate expression for h_N in terms of its GCE
counterpart that agrees with the expansion of h_N in powers of 1/N.Comment: 5 pages, RevTeX. Submitted to Phys. Rev. Let
Block-Wise Pseudo-Marginal Metropolis-Hastings
The pseudo-marginal Metropolis-Hastings approach is increasingly used for Bayesian inference in statistical models where the likelihood is analytically intractable but can be estimated unbiasedly, such as random effects models and state-space models, or for data subsampling in big data settings. In a seminal paper, Deligiannidis et al. (2015) show how the pseudo-marginal Metropolis-Hastings (PMMH) approach can be made much more e cient by correlating the underlying random numbers used to form the estimate of the likelihood at the current and proposed values of the unknown parameters. Their proposed approach greatly speeds up the standard PMMH algorithm, as it requires a much smaller number of particles to form the optimal likelihood estimate. We present a closely related alternative PMMH approach that divides the underlying random numbers mentioned above into blocks so that the likelihood estimates for the proposed and current values of the likelihood only di er by the random numbers in one block. Our approach is less general than that of Deligiannidis et al. (2015), but has the following advantages. First, it provides a more direct way to control the correlation between the logarithms of the estimates of the likelihood at the current and proposed values of the parameters. Second, the mathematical properties of the method are simplified and made more transparent compared to the treatment in Deligiannidis et al. (2015). Third, blocking is shown to be a natural way to carry out PMMH in, for example, panel data models and subsampling problems. We obtain theory and guidelines for selecting the optimal number of particles, and document large speed-ups in a panel data example and a subsampling problem
Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
It was recently pointed out that topological liquid phases arising in the
fractional quantum Hall effect (FQHE) are not required to be rotationally
invariant, as most variational wavefunctions proposed to date have been.
Instead, they possess a geometric degree of freedom corresponding to a shear
deformation that acts like an intrinsic metric. We apply this idea to a system
with an anisotropic band mass, as is intrinsically the case in many-valley
semiconductors such as AlAs and Si, or in isotropic systems like GaAs in the
presence of a tilted magnetic field, which breaks the rotational invariance. We
perform exact diagonalization calculations with periodic boundary conditions
(torus geometry) for various filling fractions in the lowest, first and second
Landau levels. In the lowest Landau level, we demonstrate that FQHE states
generally survive the breakdown of rotational invariance by moderate values of
the band mass anisotropy. At 1/3 filling, we generate a variational family of
Laughlin wavefunctions parametrized by the metric degree of freedom. We show
that the intrinsic metric of the Laughlin state adjusts as the band mass
anisotropy or the dielectric tensor are varied, while the phase remains robust.
In the n=1 Landau level, mass anisotropy drives transitions between
incompressible liquids and compressible states with charge density wave
ordering. In n>=2 Landau levels, mass anisotropy selects and enhances stripe
ordering with compatible wave vectors at partial 1/3 and 1/2 fillings.Comment: 9 pages, 8 figure
Time Dependent Floquet Theory and Absence of an Adiabatic Limit
Quantum systems subject to time periodic fields of finite amplitude, lambda,
have conventionally been handled either by low order perturbation theory, for
lambda not too large, or by exact diagonalization within a finite basis of N
states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has
been assumed. But the validity of these procedures seems questionable in view
of the fact that, as N goes to infinity, the quasienergy spectrum becomes
dense, and numerical calculations show an increasing number of weakly avoided
crossings (related in perturbation theory to high order resonances). This paper
deals with the highly non-trivial behavior of the solutions in this limit. The
Floquet states, and the associated quasienergies, become highly irregular
functions of the amplitude, lambda. The mathematical radii of convergence of
perturbation theory in lambda approach zero. There is no adiabatic limit of the
wave functions when lambda is turned on arbitrarily slowly. However, the
quasienergy becomes independent of time in this limit. We introduce a
modification of the adiabatic theorem. We explain why, in spite of the
pervasive pathologies of the Floquet states in the limit N goes to infinity,
the conventional approaches are appropriate in almost all physically
interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure
Electron Localization in the Insulating State
The insulating state of matter is characterized by the excitation spectrum,
but also by qualitative features of the electronic ground state. The insulating
ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is
localized. We give a sharp definition of the latter concept, and we show how
the two basic features stem from essentially the same formalism. Our approach
to localization is exemplified by means of a two--band Hubbard model in one
dimension. In the noninteracting limit the wavefunction localization is
measured by the spread of the Wannier orbitals.Comment: 5 pages including 3 figures, submitted to PR
Ab initio Study of Misfit Dislocations at the SiC/Si(001) Interface
The high lattice mismatched SiC/Si(001) interface was investigated by means
of combined classical and ab initio molecular dynamics. Among the several
configurations analyzed, a dislocation network pinned at the interface was
found to be the most efficient mechanism for strain relief. A detailed
description of the dislocation core is given, and the related electronic
properties are discussed for the most stable geometry: we found interface
states localized in the gap that may be a source of failure of electronic
devices
Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach
An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed
and solved in the BCS approximation. The method is applied to the t-t' Hubbard
model in two dimensions with the following results: (i) The superconducting
phase diagram at half filling is shown to provide a weak-coupling analog of the
recently proposed spin liquid state in the J_1-J_2 Heisenberg model. (ii) In
the parameter region relevant for the cuprates we have found a nontrivial
energy dependence of the gap function in the dominant d-wave pairing sector.
The hot spot effect in the angular dependence of the superconducting gap is
shown to be quite weak
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