On the Law of Equipartition for Translational Motion of Excited Molecules in Equilibrium with Thermal Radiation

1989 ◽  
Vol 44 (4) ◽  
pp. 273-277
Author(s):  
B. H. Lavenda
Keyword(s):  
Translational Motion ◽  
Excited Molecule ◽  
Temperature Limit ◽  
Stimulated Emission ◽  
High Temperature Limit ◽  
Radiation Theory ◽  
The Law ◽  
Excited Molecules ◽  
The One ◽  
Limiting Condition

Abstract Einstein’s radiation theory consists of two parts: the derivation of Planck's radiation law from a physical mechanism of absorption and emission of radiation by excited molecules that are in thermal equilibrium with the radiation field and a demonstration of the validity of the law of equipartition of energy for the translational motion of the molecules. Several incongruities are observed: Einstein could not have legitimately substituted back into his dynamical equilibrium condition, valid at any finite temperature, a limiting condition between the coefficients of absorption and stimulated emission that he obtained in the high temperature limit. His justification of the law of equipartition involves, on the one hand, treating the motion of the excited molecule as brownian motion while, on the other hand, employing special relativity to obtain an expression for the diffusion coefficient. In the former the velocity of the molecule is a stochastic variable while in the latter it is a uniform velocity. Hence equipartition does not hold for the translational motion.

scholarly journals Analytical results of the one-dimensional Hubbard model in the high-temperature limit

2001 ◽  
Vol 64 (19) ◽  
Author(s):  
I. C. Charret ◽  
E. V. Corrêa Silva ◽  
S. M. de Souza ◽  
O. Rojas Santos ◽  
M. T. Thomaz ◽  
...  
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
Temperature Limit ◽  
One Dimensional ◽  
High Temperature Limit ◽  
Analytical Results ◽  
The One

scholarly journals A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

2002 ◽  
Vol 17 (17) ◽  
pp. 2351-2368 ◽  
Author(s):  
ZENGO TSUBOI
Keyword(s):  
Bethe Ansatz ◽  
Central Charge ◽  
Lie Superalgebra ◽  
Temperature Limit ◽  
Entropy Density ◽  
Fundamental Representation ◽  
Thermodynamic Bethe Ansatz ◽  
High Temperature Limit ◽  
The One ◽  
T System

A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string hypothesis. The high temperature limit of the entropy density is expressed in terms of the solution of the osp(1|2s) version of the Q-system. In particular for the fundamental representation case, we also derive a TBA equation from the osp(1|2s) version of the T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis. The central charge is expressed by the Rogers dilogarithmic function and identified to s.

scholarly journals Thermal effects of a photon gas with a deformed Heisenberg algebra

2016 ◽  
Vol 31 (32) ◽  
pp. 1650172 ◽  
Author(s):  
R. Bufalo
Keyword(s):  
High Temperature ◽  
Thermal Effects ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Temperature Limit ◽  
Loop Order ◽  
High Temperature Limit ◽  
Photon Gas ◽  
The One ◽  
Boltzmann Law

In this paper, we have considered the thermodynamics of a photon gas subject to the presence of a minimal measurable length following from a covariant extension of the original generalized uncertainty principle (GUP). After consistently establishing a generalized dynamics, we define a GUP deformed Maxwell invariant which serves as the basis for our study. In order to highlight the GUP effects, we compute the one- and two-loop order contribution to the partition function at the high-temperature limit. Afterwards, by computing the internal energy density, we conclude that the additional terms can be seen as corrections [Formula: see text] to the Stefan–Boltzmann law due to GUP effects.

scholarly journals LOGARITHMIC CORRECTION TO SCALING FOR MULTISPIN STRINGS IN THE AdS5 BLACK HOLE BACKGROUND

2008 ◽  
Vol 23 (05) ◽  
pp. 719-727
Author(s):  
A. L. LARSEN
Keyword(s):  
Black Hole ◽  
Radial Direction ◽  
Temperature Limit ◽  
Space Time ◽  
Explicit Solutions ◽  
Logarithmic Correction ◽  
High Temperature Limit ◽  
Black Hole Background ◽  
Correction To Scaling ◽  
The One

We find new explicit solutions describing closed strings spinning with equal angular momentum in two independent planes in the AdS5 black hole space–time. These are 2n-folded strings in the radial direction and also winding m times around an angular direction. We specially consider these solutions in the long string and high temperature limit, where it is shown that there is a logarithmic correction to the scaling between energy and spin. This is similar to the one-spin case. The strings are spinning, or actually orbiting around the black hole of the AdS5 black hole space–time, similar to the solutions previously found in black hole space–times.

Law’s Contradictions

2018 ◽  
Author(s):  
Nimer Sultany
Keyword(s):  
The Other ◽  
Political Actors ◽  
Political Conflicts ◽  
Other Hand ◽  
The Law ◽  
The One

This chapter analyzes concrete Egyptian and Tunisian cases that showcase the interplay between continuity and rupture. These cases illustrate the lack of a systemic relation between law and revolution. On the one hand, the judiciary that interprets and applies the law is part of the very social and political conflicts it is supposed to resolve. On the other hand, the law is incoherent and there are often resources within the legal materials to play it both ways. Thus, the different forces at work use both continuity and rupture to advance their positions. Furthermore, legitimacy discourse mediates the contradictions between law and revolution in the experience of different legal and political actors. This mediation serves an ideological role because it presupposes a binary dichotomy between continuity and rupture, papers over law’s incoherence by reducing it to a singular voice, and reduces revolution to an event rather than a process.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

scholarly journals Quantification of Classified Nickel Species in Spent FFC Catalysts

2021 ◽  
Author(s):  
Monica Dapiaggi ◽  
Marco Alloni ◽  
Riccardo Carli ◽  
Nicola Rotiroti ◽  
Giorgia Confalonieri
Keyword(s):  
Zeolite Y ◽  
Complex Matrix ◽  
Spent Catalyst ◽  
Quick Method ◽  
Spent Catalysts ◽  
The Law ◽  
The One ◽  
Nickel Species

Abstract The paper presents a quick method for the quantification of nickel species in spent FFC catalysts; the quantification of known quantities NiO and $$\hbox{NiAl}_2\hbox{O}_{4}$$ NiAl 2 O 4 is first done in a matrix of fresh zeolite Y, and then in a complex matrix, similar to the one of a real spent catalyst. The method is carefully checked and the errors in the quantification are critically evaluated. After the validation of the method with known quantities of NiO, well below the law limit for direct re-use, a set of real spent catalysts (representative of a period of 12 months) is analysed. Graphic Abstract

Insider Trading in Israel and England, Part II

1972 ◽  
Vol 7 (3) ◽  
pp. 373-410
Author(s):  
Aharon Yoran
Keyword(s):  
Insider Trading ◽  
The Other ◽  
Fiduciary Duties ◽  
The Law ◽  
The One

It is submitted that even if the hapless outsider cannot bring an action for damages because of the existing state of the law regarding fiduciary duties and breach of statutory duties, he still has an equitable remedy of rescission of the contract based on quasi-contractual principles. The crime of fraud, under secs. 13 and 54, respectively, would be made the basis of setting the contract (of sale or purchase) aside. To support this proposition we shall explore the quasi-contractual principles which enable one contracting party, the victim of a crime committed by the other party in entering the contract, to defeat this contract.In Browning v. Morris, in an oft-quoted statement by Lord Mansfield, the following principle was declared: But, where contracts or transactions are prohibited by positive statutes, for protecting one set of men from another set of men; the one, from their situation and condition, being liable to be oppressed or imposed upon by the other; there, the parties are not in pan delicto; and in furtherance of these statutes, the person injured, after the transaction is finished and completed, may bring an action and defeat the contract.

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