scholarly journals Effusion and thermal transpiration in quantum statistics

1939 ◽  
Vol 171 (947) ◽  
pp. 469-484 ◽  
Keyword(s):  
Steady State ◽  
Relativistic Quantum ◽  
Quantum Statistics ◽  
Present Communication ◽  
Thermal Transpiration ◽  
Usual Quantum ◽  
Quantum Statistical

In a previous paper (Srivastava 1938) the author has considered the effusion phenomena in detail from the standpoint of relativistic quantum statistics. This paper will be hereafter referred to as paper I. In this, however, the effusion of the gas into vacuum was considered. In the present communication we have investigated in § 1 the molecular effusion of one gas into another at a different pressure but at the same temperature. In §§ 2-4 the effusion of one gas into another at a different temperature has been considered, giving rise to the phenomenon of thermal transpiration, and the relation between the pressures in the two chambers in the steady state has been calculated. Non-degenerate matter has been considered in § 2, degenerate matter in § 3, and effusion of degenerate into non-degenerate matter in § 4. The method adopted is similar to that utilized in paper I involving the use of the usual quantum-statistical formulae. For the sake of brevity we shall omit here the deduction of certain results and the various steps of mathematical simplification which have already featured in paper I and shall content ourselves by merely quoting the results.

scholarly journals Effusion phenomena in relativistic quantum statistics.

1938 ◽  
Vol 167 (931) ◽  
pp. 516-526 ◽  
Author(s):  
B. N. Srivastava ◽  
Meghnad N Saha
Keyword(s):  
Free Path ◽  
Present Author ◽  
Relativistic Quantum ◽  
Mean Free Path ◽  
Quantum Statistics ◽  
Present Communication ◽  
Helium Gas ◽  
The Mean

Considerable attention has been devoted in recent years to the investigation of properties of degenerate and non-degenerate matter. Quite recently the Joule-Thompson expansion of degenerate matter has been studied by Kothari (1938), while the present author (Srivastava 1938) investigated the same effect in non-degenerate matter and showed that the phenomenon of Joule-Thompson expansion may possibly serve as a means of experimentally testing the statistics obeyed by helium gas. In the present communication the effusion phenomena in degenerate and non-degenerate matter have been investigated, taking into account the effect of relativistic mechanics. In §1 the effusion of non-degenerate matter has been discussed while degenerate matter has been considered in §2. 1. Non-degenerate matter Let us consider a gas contained in a vessel having a narrow orifice on one side and let the gas escape through this orifice into a vacuum outside. We shall assume that the pressure of the gas is so low that the mean free path is much greater than the dimensions of the orifice. Under these conditions we shall calculate the amount of matter effusing out through this hole.

scholarly journals Steady-state quantum statistics of a non-Markovian atom laser. II

2003 ◽  
Vol 68 (6) ◽  
Author(s):  
A. S. Bradley ◽  
J. J. Hope ◽  
M. J. Collett
Keyword(s):  
Steady State ◽  
Quantum Statistics ◽  
Atom Laser

scholarly journals On the description of subsystems in relativistic hypersurface Bohmian mechanics

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140181 ◽  
Author(s):  
Detlef Dürr ◽  
Matthias Lienert
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Density Matrix ◽  
Relativistic Quantum ◽  
Bohmian Mechanics ◽  
Conditional Density ◽  
Relativistic Quantum Theory ◽  
Relativistic Case ◽  
Usual Quantum ◽  
Effective Wave

A candidate for a realistic relativistic quantum theory is the hypersurface Bohm–Dirac model. Its formulation uses a foliation of space–time into space-like hypersurfaces. In order to apply the theory and to make contact with the usual quantum formalism, one needs a framework for the description of subsystems. The presence of spin together with the foliation renders the subsystem description more complicated than in the non-relativistic case with spin. In this paper, we provide such a framework in terms of an appropriate conditional density matrix and an effective wave function as well as clarify their relation, thereby generalizing previous subsystem descriptions in the non-relativistic case.

scholarly journals On the Drift Velocity of Electrons in a Gas

1972 ◽  
Vol 25 (3) ◽  
pp. 329
Author(s):  
SL Paveri-Fontana
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Drift Velocity ◽  
Isotropic Scattering ◽  
Uniform Electric Field ◽  
Present Communication ◽  
Steady State Distribution ◽  
State Distribution ◽  
Neutral Gas

In a recent paper, Crompton, Elford, and Robertson (1970; hereafter referred to as CER) considered certain questions concerning the steady-state distribution of electrons moving in a neutral gas under the influence of a uniform electric field E. The present communication comments on some aspects of the error discussion in the Appendix of the paper by CER. The analysis will be restricted to the case of isotropic scattering.

scholarly journals Thermal transpiration of a dissociating gas

1940 ◽  
Vol 175 (963) ◽  
pp. 474-483 ◽  
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Absolute Magnitude ◽  
Mass Action ◽  
Law Of Mass Action ◽  
Thermodynamical Equilibrium ◽  
Thermal Transpiration ◽  
Different Temperatures ◽  
The Absolute ◽  
Narrow Opening

In this paper the thermal transpiration of a dissociating gas has been investigated theoretically for two chambers maintained at different temperatures and communicating with each other through a narrow opening. It has been shown that the condition of thermodynamical equilibrium and the usual transpiration relation for each constituent cannot both be satisfied simultaneously. In § 2 the problem has been treated rigorously from the viewpoint of a steady state. Expressions have been worked out showing how the law of mass action suffers modification in this case. Expressions have also been deduced for the atomic and molecular concentrations in the two chambers and the modified transpiration relation is stated. In § 3 an approximate solution of the problem has been given which is based on the assumption of thermodynamical equilibrium in each chamber. Expressions have been deduced for the absolute magnitude as well as the ratio of the atomic or molecular concentrations in the two chambers in the general case and some limiting cases. Finally, the relative merits and demerits of both the treatments have been clearly set forth.

EFFECT OF MAXIMUM MOMENTUM ON QUANTUM MECHANICAL SCATTERING AND BOUND STATES

2013 ◽  
Vol 28 (15) ◽  
pp. 1350061 ◽  
Author(s):  
CHEE-LEONG CHING ◽  
RAJESH R. PARWANI
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Position Uncertainty ◽  
Exact Position ◽  
Usual Quantum ◽  
Quantum Mechanical Scattering ◽  
Mechanical Scattering

We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.

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