The chemical potential in terms of n‐particle direct correlation functions

1991 ◽  
Vol 94 (3) ◽  
pp. 2370-2371 ◽  
Author(s):  
Phil Attard
Keyword(s):  
Correlation Functions ◽  
Chemical Potential

scholarly journals Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

2018 ◽  
Vol 175 ◽  
pp. 05003 ◽  
Author(s):  
Michael Wagman
Keyword(s):  
Lattice Qcd ◽  
Correlation Functions ◽  
Chemical Potential ◽  
Time Correlation ◽  
Time Interval ◽  
Signal To Noise ◽  
Complex Phase ◽  
Sign Problem ◽  
Heavy Tailed ◽  
Potential Sign

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.

scholarly journals Coherent Transport in Periodically Driven Mesoscopic Conductors: From Scattering Amplitudes to Quantum Thermodynamics

2020 ◽  
Vol 75 (5) ◽  
pp. 483-500
Author(s):  
Kay Brandner
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Frequency Noise ◽  
Perturbation Scheme ◽  
Quantum Thermodynamics ◽  
Mean Values ◽  
Periodically Driven ◽  
The Mean

AbstractScattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic fields. Our approach is based on an extension of the conventional Lippmann–Schwinger formalism to systems with a periodically time-dependent Hamiltonian. As a key result, we obtain a systematic perturbation scheme for the Floquet scattering amplitudes that describes the transition of a transport carrier through a periodically driven sample. Within a general multi-terminal setup, we derive microscopic expressions for the mean values and time-integrated correlation functions, or zero-frequency noise, of matter and energy currents, thus recovering the results of earlier studies in a unifying framework. We show that this framework is inherently consistent with the first and the second law of thermodynamics and prove that the mean rate of entropy production vanishes only if all currents in the system are zero. As an application, we derive a generalized Green–Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. Finally, we discuss potential topics for future studies and further reaching applications of the Floquet scattering approach to quantum transport in stochastic and quantum thermodynamics.

scholarly journals A window on infrared QCD with small expansion parameters

2021 ◽  
Author(s):  
Marcela Peláez ◽  
Urko Reinosa ◽  
Julien Serreau ◽  
Matthieu Tissier ◽  
Nicolas Wschebor
Keyword(s):  
Correlation Functions ◽  
Chemical Potential ◽  
Landau Gauge ◽  
Spontaneous Breaking ◽  
Tree Level ◽  
Coupling Constant ◽  
Long Distance ◽  
Gauge Sector ◽  
Small Parameters ◽  
Distance Properties

Abstract Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector — defined, e.g., in the Taylor scheme— remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

scholarly journals Time and Temperature Dependent Correlation Functions of the One-Dimensional Impenetrable Electron Gas

1998 ◽  
Vol 12 (23) ◽  
pp. 2409-2433 ◽  
Author(s):  
F. Göhmann ◽  
A. G. Izergin ◽  
V. E. Korepin ◽  
A. G. Pronko
Keyword(s):  
Correlation Functions ◽  
Chemical Potential ◽  
Hilbert Problem ◽  
Electron Gas ◽  
Local Fields ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Asymptotic Expressions ◽  
Long Time ◽  
The One

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.

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