arXiv subjects

E. Arias

Publications and source records attributed to E. Arias.

10 recordsLinked to original sources

arXiv2024

The Casimir-Lifshitz formula for rectangular dielectric waveguide

We analyze the Casimir-Lifshitz effect associated with the electromagnetic field in the presence of a rectangular waveguide consisting of two distinct dielectric materials in a $(3+1)$-dimensional spacetime. We employ the surface mode technique to derive a generalized Lifshitz formula for this specific geometry. Our formulation accounts for the unique dielectric properties of the materials composing the waveguide, leading to a precise calculation of the Casimir-Lifshitz energy. In the asymptotic limit, our results recover the classical expressions for perfect reflecting boundaries. This work extends the applicability of the Lifshitz formula to more complex systems and provides valuable insights into the influence of dielectric materials on the electromagnetic Casimir effect.

quant-ph↗

arXiv2023

The vacuum energy with non-ideal boundary conditions via an approximate functional equation

We discuss the vacuum energy of a quantized scalar field in the presence of classical surfaces, defining bounded domains $\Omega \subset {\mathbb{R}}^{d}$, where the field satisfies ideal or non-ideal boundary conditions. For the electromagnetic case, this situation describes the conductivity correction to the zero-point energy. Using an analytic regularization procedure, we obtain the vacuum energy for a massless scalar field at zero temperature in the presence of a slab geometry $\Omega=\mathbb R^{d-1}\times[0, L]$ with Dirichlet boundary conditions. To discuss the case of non-ideal boundary conditions, we employ an asymptotic expansion, based on an approximate functional equation for the Riemann zeta-function, where finite sums outside their original domain of convergence are defined. Finally, to obtain the Casimir energy for a massless scalar field in the presence of a rectangular box, with lengths $L_{1}$ and $L_{2}$, i.e., $\Omega=[0,L_{1}]\times[0,L_{2}]$ with non-ideal boundary conditions, we employ an approximate functional equation of the Epstein zeta-function.

math-ph↗

arXiv2019

Enhancement of efficiency in the Dicke model quantum heat engine

We analyze a quantum heat engine described by the full Dicke model. The system exhibit quantum phase transitions under certain conditions. We consider the system performing a Stirling thermodynamic cycle. We obtain an enhancement of efficiency when during the cycle the coupling parameter cross a critical value. We analyze the effect of unbalance between rotating and counter-rotating terms in the model. The maximum efficiency is obtained when the contributions of the counter-rotating and rotating terms are equal. The relation between ground state degeneracy, related to the quantum phase transition, and maximum efficiency is investigated.

quant-ph↗

arXiv2016

Boundary effects on radiative processes of two entangled atoms

We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat mirrors. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transitions rates from the entangled states to the collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between the atoms. Next, we consider the presence of perfect mirrors and impose Dirichlet boundary conditions on such surfaces. In the presence of a single mirror the transition rate for the symmetric state undergoes a slight reduction, whereas for the antisymmetric state our results indicate a slightly enhancement. Finally, we investigate the effect of multiple reflections by two perfect mirrors on the transition rates.

quant-ph↗

arXiv2014

Relativistic Bose-Einstein condensation with disorder

We investigate the thermodynamics of a self-interacting relativistic charged scalar field in the presence of weak disorder. We consider quenched disorder which couples linearly to the mass of the scalar field. After performing noise averages over the free energy of the system, we find that disorder increases the mean-field critical temperature for Bose-Einstein condensation at finite density. The effect of disorder on the temperature dependence of the chemical potential for a fixed charge density is investigated. Significant differences from the mean-field temperature dependence of the chemical potential are observed as the strength of the noise intensity increases. Finally, the temperature dependence of the chemical potential with fixed total charge and entropy is investigated. It is found that there is no Bose-Einstein condensation for a fixed charge to entropy ratio in the presence of weak disorder. The possible relevance of the findings in the present paper in different areas is discussed.

hep-th↗

arXiv2014

Casimir Energy Corrections by Light-Cone Fluctuations

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations we introduce a space-time dependent random coefficient in the Klein-Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance $a$. The correction to the renormalized vacuum energy density between the plates goes as $1/a^{8}$ instead of the usual $1/a^{4}$ dependence for the free case. In turn we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.

hep-th↗

arXiv2011

Thermal Radiation from a Fluctuating Event Horizon

We consider a pointlike two-level system undergoing uniformly accelerated motion. We evaluate the transition probability for a finite time interval of this system coupled to a massless scalar field near a fluctuating event horizon. Horizon fluctuations are modeled using a random noise which generates light-cone fluctuations. We study the case of centered, stationary and Gaussian random processes. The transition probability of the system is obtained from the positive-frequency Wightman function calculated to one loop order in the noise averaging process. Our results show that the fluctuating horizon modifies the thermal radiation but leaves unchanged the temperature associated with the acceleration.

hep-th↗

arXiv2011

An analog fluid model for some tachyonic effects in field theory

We consider the sound radiation from an acoustic point-like source moving along a supersonic ("space-like") trajectory in a fluid at rest. We call it an acoustic "tachyonic" source. We describe the radiation emitted by this supersonic source. After quantizing the acoustic perturbations, we present the distribution of phonons generated by this classical tachyonic source and the classical wave interference pattern.

hep-th↗

arXiv2011

Scalar Quantum Field Theory in Disordered Media

A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Green's function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $λϕ^{4}$ self-interacting theory with a frequency-dependent coupling.

hep-th↗

arXiv2010

The Bekenstein Bound in Asymptotically Free Field Theory

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E} \leq 2 πR$, where $R$ stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound on the specific entropy in the asymptotically free side of the Euclidean $(λ\,ϕ^{\,4})_{d}$ self-interacting scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature $β^{\,-1}$ and defined in a compact spatial region without boundaries. Using the effective potential, we presented an exhaustive study of the thermodynamic of the model. For low and high temperatures the system presents a condensate. We obtain also the renormalized mean energy $E$ and entropy $S$ for the system. With these quantities, we shown in which situations the specific entropy satisfies the quantum bound.

hep-th↗