scholarly journals Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Maciej Łebek ◽  
Pawel Jakubczyk
Keyword(s):  
Casimir Effect ◽  
Quantum Phase Transitions ◽  
Scaling Limit ◽  
Mean Field ◽  
Temperature Phase ◽  
Casimir Forces ◽  
Lattice Systems ◽  
Slab Geometry ◽  
Anisotropic Systems ◽  
Spatial Dimensionality

We analyze the thermodynamic Casimir effect in strongly anisotropic systems from the vectorial N\to\inftyN→∞ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality dd in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion relation and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality d\in (\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dotsd∈(52,4)∪(6,8)∪(10,12)∪… and attractive for d\in (4,6)\cup (8,10)\cup \dotsd∈(4,6)∪(8,10)∪…. We argue, that for d\in\{4,6,8\dots\}d∈{4,6,8…} the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by 1/N>01/N>0 and possible realizations in the contexts of optical lattice systems and quantum phase transitions.

scholarly journals Thermal Casimir effect with general boundary conditions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
L. Santamaría-Sanz ◽  
M. Donaire ◽  
M. Tello-Fraile
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Quantum Field ◽  
Quantum Vacuum ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Thermal Correction ◽  
Frequency Independent ◽  
Scalar Quantum

Abstract In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

scholarly journals The Smoluchowski Ensemble—Statistical Mechanics of Aggregation

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1181
Author(s):  
Themis Matsoukas
Keyword(s):  
Sol Gel ◽  
Scaling Limit ◽  
Mean Field ◽  
Central Element ◽  
Field Approximation ◽  
Fixed Number ◽  
Mean Field Approximation ◽  
The Mean ◽  
Sol Gel Transition ◽  
The Stability

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

INTERACTING BOSONIC ATOMS WITH RANDOM POTENTIAL IN OPTICAL LATTICES

2009 ◽  
Vol 23 (11) ◽  
pp. 1391-1404
Author(s):  
WEI LIU ◽  
JIAN-YANG ZHU
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field Theory ◽  
Mean Field ◽  
Temperature Phase ◽  
Optical Parameters ◽  
Xxz Model ◽  
Bose Glass ◽  
The Mean ◽  
Bosonic Atoms

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder.

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