scholarly journals Low Temperature Expansion in the Lifshitz Formula

2014 ◽  
Vol 2014 ◽  
pp. 1-34 ◽  
Author(s):  
M. Bordag
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Asymptotic Expansions ◽  
Casimir Effect ◽  
Basic Method ◽  
Temperature Expansion ◽  
Starting Point ◽  
Unified Description

The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We rederive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the asymptotic expansions forT→0. The paper includes the derivations and should provide a self-contained representation.

scholarly journals Low-temperature expansion of the Casimir–Polder free energy for an atom interacting with a conductive plane

2019 ◽  
Vol 34 (02) ◽  
pp. 1950008 ◽  
Author(s):  
N. Khusnutdinov ◽  
N. Emelianova
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Second Order ◽  
Symmetric Form ◽  
Temperature Expansion ◽  
Tm Mode ◽  
Plane System

The low-temperature expansion of the free energy of an atom/plane system is considered for a general symmetric form of the tensor conductivity of the plane. It is shown that the first correction is proportional to the second order of the temperature [Formula: see text] and comes from the TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.

scholarly journals The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 70
Author(s):  
Nail Khusnutdinov ◽  
Natalia Emelianova
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Chemical Potential ◽  
Fermi Velocity ◽  
Thermal Correction ◽  
Temperature Expansion ◽  
Poisson Representation ◽  
Zero Values ◽  
Gap Parameter ◽  
Exact Equality

We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential μ and mass gap parameter m. The key role plays the dependence of graphene conductivities on the μ and m. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For μ>m, the thermal correction ∼T2, and for μ<m, we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction ∼T5. In the case of exact equality μ=m, the correction ∼T. This point is unstable, and the system falls to the regime with μ>m or μ<m. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system.

EPSTEIN-FUNCTION ANALYSIS OF THE CASIMIR EFFECT AT FINITE TEMPERATURE FOR MASSIVE FIELDS

1992 ◽  
Vol 07 (29) ◽  
pp. 7365-7399 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Finite Temperature ◽  
Dirichlet Boundary ◽  
Casimir Effect ◽  
Function Analysis ◽  
Zeta Functions ◽  
Dirichlet Boundary Conditions ◽  
Bosonic Field ◽  
Arbitrary Dimensions

The Casimir free energy for a massive bosonic field subject to Dirichlet boundary conditions on hypercuboids of arbitrary dimensions is evaluated in the form of power and exponential expansions for the high- and low-temperature limits, respectively, with the aid of both homogeneous and inhomogeneous multidimensional Epstein zeta functions.

scholarly journals SUPER-RADIANCE AND THE UNSTABLE PHOTON OSCILLATOR

2001 ◽  
Vol 15 (05) ◽  
pp. 537-548 ◽  
Author(s):  
S. SIVASUBRAMANIAN ◽  
A. WIDOM ◽  
Y. N. SRIVASTAVA
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Low Temperature ◽  
Harmonic Oscillator ◽  
Casimir Effect ◽  
Dipole Moments ◽  
Random Force ◽  
Electric Dipole Moments ◽  
Damped Oscillator ◽  
Strongly Damped

If the damping of a simple harmonic oscillator from a thermally random force is sufficiently strong, then the oscillator may become unstable. For a photon oscillator (radiatively damped by electric dipole moments), the instability leads to a low temperature Hepp–Lieb–Preparata super-radiant phase transition. The stable oscillator regime is described by the free energy of the conventional Casimir effect. The unstable (strongly damped) oscillator has a free energy corresponding to Dicke super-radiance.

SAMPL7 TrimerTrip Host-Guest Binding Poses and Binding Affinities from Spherical-Coordinates-Biased Simulations

2020 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Computational Modelling ◽  
Free Energy Calculations ◽  
Energy Estimates ◽  
Binding Affinities ◽  
Spherical Coordinates ◽  
Collective Variables ◽  
Guest Binding ◽  
Starting Point ◽  
Sampl Challenge

Host-guest binding remains a major challenge in modern computational modelling. The newest 7<sup>th</sup> statistical assessment of the modeling of proteins and ligands (SAMPL) challenge contains a new series of host-guest systems. The TrimerTrip host binds to 16 structurally diverse guests. Previously, we have successfully employed the spherical coordinates as the collective variables coupled with the enhanced sampling technique metadynamics to enhance the sampling of the binding/unbinding event, search for possible binding poses and predict the binding affinities in all three host-guest binding cases of the 6<sup>th</sup> SAMPL challenge. In this work, we employed the same protocol to investigate the TrimerTrip host in the SAMPL7 challenge. As no binding pose is provided by the SAMPL7 host, our simulations initiate from randomly selected configurations and are proceeded long enough to obtain converged free energy estimates and search for possible binding poses. The predicted binding affinities are in good agreement with the experimental reference, and the obtained binding poses serve as a nice starting point for end-point or alchemical free energy calculations.

Low-temperature expansion in the d = 4 Ising model

1992 ◽  
Vol 374 (3) ◽  
pp. 647-666 ◽  
Author(s):  
C. Vohwinkel ◽  
P. Weisz
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

scholarly journals CASIMIR ENERGY OF A DILUTE DIELECTRIC BALL AT ZERO AND FINITE TEMPERATURE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 790-793 ◽  
Author(s):  
V. V. NESTERENKO ◽  
G. LAMBIASE ◽  
G. SCARPETTA
Keyword(s):  
Free Energy ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
High Temperature ◽  
Finite Temperature ◽  
Bessel Functions ◽  
Thermodynamic Characteristics ◽  
Casimir Energy ◽  
Addition Theorem ◽  
Temperature Expansion

The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated. The T3-term in the low temperature expansion of the free energy is recovered (this term has been lost in our previous calculations).

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