A temperature-dependent upper bound on partial wave contributions to the second virial coefficient in the weak coupling limit

1978 ◽  
Vol 2 (6) ◽  
pp. 435-444
Author(s):  
S. N. Biswas ◽  
K. Datta
Keyword(s):  
Partial Wave ◽  
Upper Bound ◽  
Weak Coupling ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Weak Coupling Limit ◽  
Temperature Dependent

scholarly journals HIGH AND LOW TEMPERATURE BEHAVIOR OF A QUANTUM GROUP FERMION GAS

1996 ◽  
Vol 11 (29) ◽  
pp. 2325-2333 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Quantum Group ◽  
Upper Bound ◽  
Low Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Behavior ◽  
Spatial Dimensions ◽  
Fermion Gas

We consider the simplest SU q(2) invariant fermionic Hamiltonian and calculate the low and high temperature behavior for the two distinct cases q>1 and q<1. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to q≠1. At high temperatures we find that the sign of the second virial coefficient depends on q, and vanishes at q=1.96. An important consequence of this fact is that the parameter q connects the fermionic and bosonic regions, showing therefore that SU q(2) fermions exhibit fractional statistics in three spatial dimensions.

CONTINUOUS UPPER BOUND ON THE GROUND-STATE ENERGY OF THE FRÖHLICH POLARON

1994 ◽  
Vol 08 (08n09) ◽  
pp. 553-560 ◽  
Author(s):  
A. V. SOLDATOV
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Coherent States ◽  
Weak Coupling ◽  
State Energy ◽  
Coupling Parameter ◽  
Weak Coupling Limit

The upper bound on the ground-state energy for the Fröhlich polaron is derived by means of a new version of variational principle based on the Wick symbols formalism and the coherent states theory. The bound is continuous in some respect, i.e. it is valid for all values of coupling parameter including the intermediate regions. Asymptotic behavior of the bound for the weak coupling limit and for the strong coupling limit provides, in general, lower values than well-known existing bounds. The bound can be readily generalized for the case of nonzero magnetic field.

scholarly journals Predicting second virial coefficients of organic and inorganic compounds using Gaussian process regression

2021 ◽  
Vol 23 (4) ◽  
pp. 2891-2898
Author(s):  
Miruna T. Cretu ◽  
Jesús Pérez-Ríos
Keyword(s):  
Gaussian Process ◽  
Virial Coefficient ◽  
Inorganic Compounds ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Gaussian Process Regression ◽  
Temperature Dependent ◽  
Second Virial Coefficients ◽  
Molecular Features

Intuitive and accessible molecular features are used to predict the temperature-dependent second virial coefficient of organic and inorganic compounds with Gaussian process regression.

INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2593-2600 ◽  
Author(s):  
JIANXIANG TIAN
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Critical Properties ◽  
Temperature Dependent ◽  
Packing Factor ◽  
Third Virial Coefficient ◽  
Real Fluids

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

scholarly journals An obstacle to sub-AdS holography for SYK-like models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang ◽  
Yingfei Gu ◽  
Alexei Kitaev
Keyword(s):  
Lyapunov Exponent ◽  
Weak Coupling ◽  
Kinetic Coefficient ◽  
Weak Coupling Limit ◽  
Branching Time ◽  
Quasiparticle Lifetime

Abstract We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

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