Dependence of the existence of thermal equilibrium on the number of particles at low temperatures

2007 ◽  
Vol 75 (5) ◽  
pp. 431-433 ◽  
Author(s):  
X. Wang ◽  
Q. H. Liu ◽  
W. Dong
Keyword(s):  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Number Of Particles

Thermal Equilibrium Between LiquidHe3and Powdered Cerium Magnesium Nitrate at Very Low Temperatures

1966 ◽  
Vol 16 (7) ◽  
pp. 273-275 ◽  
Author(s):  
W. R. Abel ◽  
A. C. Anderson ◽  
W. C. Black ◽  
J. C. Wheatley
Keyword(s):  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Magnesium Nitrate

The thermal conductivity of metals

1938 ◽  
Vol 34 (3) ◽  
pp. 474-497 ◽  
Author(s):  
R. E. B. Makinson
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Major Part ◽  
Lattice Energy ◽  
Conduction Electrons ◽  
Electronic Heat ◽  
Lattice Waves ◽  
Lattice Heat

The methods used to measure separately the electronic and lattice heat conductivities κeand κgin a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κeand for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratioLe= κe/σTas a function ofT, both for the monovalent metals and for a model metal with 1·8 × 10−2conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κeand κgas functions ofTare given in both cases, and these, together with a comparison of the observed Lorentz ratio andLe, show that in the monovalent metals κgis unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.

Thermal field theory

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Statistical Physics ◽  
Thermal Field ◽  
Scalar Fields ◽  
Temperature Dependent ◽  
Scalar Particles ◽  
Debye Mass

After a review of the calculational approaches, the free energy of scalar particles in thermal equilibrium is calculated. The IR behaviour of mass-less scalar fields is examined, finding that a resummation of IR divergent terms is necessary. In general, particles acquire a temperature-dependent (Debye) mass, while symmetries of the Lagrangian may be hidden at low temperatures. In an appendix, the basics of equilibrium statistical physics is reviewe

The properties of a perfect Einstein-Bose gas at low temperatures

1938 ◽  
Vol 34 (4) ◽  
pp. 573-576 ◽  
Author(s):  
R. H. Fowler ◽  
H. Jones
Keyword(s):  
Condensed Phase ◽  
Low Temperatures ◽  
Unit Volume ◽  
Bose Gas ◽  
The Other ◽  
Perfect Gas ◽  
Recent Letter ◽  
Bose Statistics ◽  
Image Position ◽  
Number Of Particles

In a recent letter to Nature F. London(3) has called attention to a discontinuity in the derivative dCV/dT of the specific heat with respect to temperature which arises in a perfect Einstein-Bose gas at low temperatures. When discussing the properties of a perfect gas satisfying the Bose statistics, Einstein(1) remarked that at low temperatures something resembling a condensed phase should appear. The temperature at which this condensation should begin is given by the equationwhere n is the number of particles of mass m per unit volume and the other symbols have their usual significance.

Notizen: A Note on the Off-Diagonal Elements of the Density Matrix in Thermal Equilibrium and Thermal Radiation

1980 ◽  
Vol 35 (9) ◽  
pp. 992-994
Author(s):  
D. H. Sutter
Keyword(s):  
Density Matrix ◽  
Thermal Radiation ◽  
Gas Phase ◽  
Spontaneous Emission ◽  
Thermal Equilibrium ◽  
Quantitative Comparison ◽  
The One ◽  
Molecular Ensemble ◽  
Number Of Particles

Abstract A closer look at the off-diagonal elements of the density matrix of a thermal gas phase molecular ensemble reveals, that they lead to a contribution to thermal radiation which increases in power proportional to the number of particles. A quantitative comparison of this contribution to the one originating from spontaneous emission is given.

scholarly journals Evaluation of the thermodynamics of a four level system using canonical density matrix method

2011 ◽  
Vol 33 (4) ◽  
pp. 91-108
Author(s):  
Aladunjoye A. Awoga ◽  
Akpan A. Ikot ◽  
Eno E. Ituen ◽  
Louis E. Akpabio
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Density Matrix ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Kronecker Product ◽  
Entire System ◽  
Level System ◽  
Laws Of Thermodynamics ◽  
Product Method

Abstract We consider a four-level system with two subsystems coupled by weak interaction. The system is in thermal equilibrium. The thermodynamics of the system, namely internal energy, free energy, entropy and heat capacity, are evaluated using the canonical density matrix by two methods. First by Kronecker product method and later by treating the subsystems separately and then adding the evaluated thermodynamic properties of each subsystem. It is discovered that both methods yield the same result, the results obey the laws of thermodynamics and are the same as earlier obtained results. The results also show that each level of the subsystems introduces a new degree of freedom and increases the entropy of the entire system. We also found that the four-level system predicts a linear relationship between heat capacity and temperature at very low temperatures just as in metals. Our numerical results show the same trend.

BOSE–EINSTEIN QUASICONDENSATION IN 2D SYSTEMS

2005 ◽  
Vol 19 (17) ◽  
pp. 821-827
Author(s):  
M. CRISAN ◽  
I. GROSU
Keyword(s):  
Correlation Function ◽  
Critical Temperature ◽  
Finite Number ◽  
Low Temperatures ◽  
2D Systems ◽  
Two Dimensional ◽  
Momentum Effect ◽  
Temperature Correlation ◽  
Bose Einstein ◽  
Number Of Particles

We calculate the finite temperature correlation function, the coherence length and the critical temperature for a two-dimensional (2D) bosonic system, which presents the quasicondensation (a finite number of occupied states with p0≠0 momentum) effect at very low temperatures. This state, discovered experimentally, appear below a critical temperature for a finite number of particles.

Stereo Electron Microscopy Applied to High Resolution Freeze-Etch Replicas

1970 ◽  
Vol 28 ◽  
pp. 306-307
Author(s):  
L. Andrew Staehelin
Keyword(s):  
Electron Microscopy ◽  
Plastic Deformation ◽  
High Resolution ◽  
Smooth Surfaces ◽  
Small Particles ◽  
Membrane Surfaces ◽  
Wide Acceptance ◽  
New Information ◽  
Number Of Particles ◽  
Small Holes

Freeze-etched membranes usually appear as relatively smooth surfaces covered with numerous small particles and a few small holes (Fig. 1). In 1966 Branton (1“) suggested that these surfaces represent split inner mem¬brane faces and not true external membrane surfaces. His theory has now gained wide acceptance partly due to new information obtained from double replicas of freeze-cleaved specimens (2,3) and from freeze-etch experi¬ments with surface labeled membranes (4). While theses studies have fur¬ther substantiated the basic idea of membrane splitting and have shown clearly which membrane faces are complementary to each other, they have left the question open, why the replicated membrane faces usually exhibit con¬siderably fewer holes than particles. According to Branton's theory the number of holes should on the average equal the number of particles. The absence of these holes can be explained in either of two ways: a) it is possible that no holes are formed during the cleaving process e.g. due to plastic deformation (5); b) holes may arise during the cleaving process but remain undetected because of inadequate replication and microscope techniques.

Interpretation of irradiation-induced changes in electron diffractograms and images of extinction contours at low temperatures

1984 ◽  
Vol 42 ◽  
pp. 268-269
Author(s):  
E. Knapek ◽  
H. Formanek ◽  
G. Lefranc ◽  
I. Dietrich
Keyword(s):  
Low Temperatures ◽  
Carbon Films ◽  
Organic Crystals ◽  
Wide Spread ◽  
Lens System ◽  
Preparation Conditions ◽  
Thin Carbon ◽  
Electron Diffractograms ◽  
Diffraction Patterns ◽  
Induced Changes

A few years ago results on cryoprotection of L-valine were reported, where the values of the critical fluence De i.e, the electron exposure which decreases the intensity of the diffraction reflections by a factor e, amounted to the order of 2000 + 1000 e/nm2. In the meantime a discrepancy arose, since several groups published De values between 100 e/nm2 and 1200 e/nm2 /1 - 4/. This disagreement and particularly the wide spread of the results induced us to investigate more thoroughly the behaviour of organic crystals at very low temperatures during electron irradiation.For this purpose large L-valine crystals with homogenuous thickness were deposited on holey carbon films, thin carbon films or Au-coated holey carbon films. These specimens were cooled down to nearly liquid helium temperature in an electron microscope with a superconducting lens system and irradiated with 200 keU-electrons. The progress of radiation damage under different preparation conditions has been observed with series of electron diffraction patterns and direct images of extinction contours.

Radiation Damage of Support Films

1981 ◽  
Vol 39 ◽  
pp. 28-29
Author(s):  
H.A. Cohen ◽  
W. Chiu
Keyword(s):  
Transfer Function ◽  
Low Temperatures ◽  
Carbon Support ◽  
Contrast Transfer Function ◽  
Electron Dose ◽  
Imaging Parameters ◽  
Negative Stain ◽  
Phase Corrections ◽  
Two Parameters ◽  
Medium Dose

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

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