scholarly journals Revisiting the Casimir energy with general boundary conditions and applications in 1D crystals

2020 ◽  
Vol 35 (03) ◽  
pp. 2040018 ◽  
Author(s):  
J. M. Muñoz-Castañeda ◽  
M. Bordag ◽  
L. Santamaría-Sanz
Keyword(s):  
Boundary Conditions ◽  
Vacuum Energy ◽  
Periodic Potential ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Quantum Vacuum ◽  
General Boundary Conditions ◽  
One Dimensional ◽  
Infinite Array ◽  
Dimensional Crystal

We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.

scholarly journals Field Fluctuations and Casimir Energy of 1D-Fermions

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 643
Author(s):  
Manuel Donaire ◽  
José María Muñoz-Castañeda ◽  
Luis Miguel Nieto ◽  
Marcos Tello-Fraile
Keyword(s):  
Vacuum Energy ◽  
Normal Modes ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Dirac Field ◽  
Edge States ◽  
Vacuum Fluctuations ◽  
One Dimensional ◽  
Mass Gap ◽  
Field Fluctuations

We investigate the self-adjoint extensions of the Dirac operator of a massive one-dimensional field of mass m confined in a finite filament of length L. We compute the spectrum of vacuum fluctuations of the Dirac field under the most general dispersionless boundary conditions. We identify its edge states in the mass gap within a set of values of the boundary parameters, and compute the Casimir energy of the discrete normal modes. Two limit cases are considered, namely, that of light fermions with m L ≪ 1 , and that of heavy fermions for which m L ≫ 1 . It is found that both positive and negative energies are obtained for different sets of values of the boundary parameters. As a consequence of our calculation we demonstrate that the sign of the quantum vacuum energy is not fixed for exchange-symmetric plates (parity-invariant configurations), unlike for electromagnetic and scalar fields.

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 How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

2007 ◽  
Vol 40 (35) ◽  
pp. 10935-10943 ◽  
Author(s):  
Kimball A Milton ◽  
Prachi Parashar ◽  
K V Shajesh ◽  
Jef Wagner
Keyword(s):  
Vacuum Energy ◽  
Casimir Energy ◽  
Gravitational Acceleration ◽  
Quantum Vacuum

scholarly journals THE FINITE VACUUM ENERGY FOR SPINOR, SCALAR AND VECTOR FIELDS

1995 ◽  
Vol 10 (16) ◽  
pp. 2333-2347
Author(s):  
N.N. SHTYKOV
Keyword(s):  
Physical Model ◽  
Vector Fields ◽  
Vacuum Energy ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Divergent Part ◽  
Scalar And Vector Fields ◽  
Massive Spinor ◽  
The One

We compute the one-loop potential (the Casimir energy) for scalar fields with coupling ξR and massive spinor and vector fields on the spaces Rm+1×Y with Y=SN, CP2. We find that in most of the models a divergent part of the Casimir energy on even-dimensional spaces is canceled by means of the appropriate values of ξ, msp, mv. As a physical model we consider spinor electrodynamics on four-dimensional product manifolds and show that the Casimir energy is finite on R1×S3, R3×S1 and R2×S2 for msp=0, msp=0 and [Formula: see text] respectively.

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