VACUUM ENERGY IN SPHERICAL DOMAINS: WKB AND UNIFORM ASYMPTOTIC EXPANSIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4129-4146 ◽  
Author(s):  
AUGUST ROMEO
Keyword(s):  
Zeta Function ◽  
Asymptotic Expansions ◽  
Zero Point ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Point Energy ◽  
Dimensional Dependence ◽  
Spherical Domains ◽  
Spectral Zeta Function ◽  
Uniform Asymptotic Expansions

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional spherical region. While some insight is offered into the dimensional dependence of the WKB approximations by examining the residues of the spectral-zeta-function poles, a mode-sum technique based on an integral representation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.’s).

scholarly journals ZERO-POINT ENERGY OF MASSLESS SCALAR FIELDS IN THE PRESENCE OF SOFT AND SEMIHARD BOUNDARIES IN D DIMENSIONS

1999 ◽  
Vol 14 (13) ◽  
pp. 2077-2089 ◽  
Author(s):  
F. CARUSO ◽  
R. DE PAOLA ◽  
N. F. SVAITER
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Zero Point ◽  
Scalar Fields ◽  
Flat Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Zero Point Energy ◽  
Point Energy ◽  
Renormalized Energy

The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–time is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on D for the cases of "hard" and "soft/semihard" boundaries are compared.

scholarly journals Casimir energy corrections by light-cone fluctuations

2014 ◽  
Vol 29 (05) ◽  
pp. 1450024 ◽  
Author(s):  
E. Arias ◽  
J. G. Dueñas ◽  
N. F. Svaiter ◽  
C. H. G. Bessa ◽  
G. Menezes
Keyword(s):  
Light Cone ◽  
Zero Point ◽  
Casimir Energy ◽  
Vacuum Energy Density ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
Point Energy ◽  
Klein Gordon ◽  
Free Case

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/a8 instead of the usual 1/a4 dependence for the free case. In turn, we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.

scholarly journals Riemann zeta zeros and zero-point energy

2014 ◽  
Vol 29 (09) ◽  
pp. 1450051 ◽  
Author(s):  
J. G. Dueñas ◽  
N. F. Svaiter
Keyword(s):  
Scalar Field ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Vacuum Energy ◽  
Zero Point ◽  
Point Energy ◽  
Nontrivial Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Adjoint Operators

The sequence of nontrivial zeros of the Riemann zeta function is zeta regularizable. Therefore, systems with countably infinite number of degrees of freedom described by self-adjoint operators whose spectra is given by this sequence admit a functional integral formulation. We discuss the consequences of the existence of such self-adjoint operators in field theory framework. We assume that they act on a massive scalar field coupled to a background field in a (d+1)-dimensional flat space–time where the scalar field is confined to the interval [0, a] in one of its dimensions and there are no restrictions in the other dimensions. The renormalized zero-point energy of this system is presented using techniques of dimensional and analytic regularization. In even-dimensional space–time, the series that defines the regularized vacuum energy is finite. For the odd-dimensional case, to obtain a finite vacuum energy per unit area, we are forced to introduce mass counterterms. A Riemann mass appears, which is the correction to the mass of the field generated by the nontrivial zeros of the Riemann zeta function.

scholarly journals Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

2014 ◽  
Vol 29 (35) ◽  
pp. 1450181
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Function Method ◽  
Casimir Energy ◽  
Function Technique ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Epstein Zeta Function ◽  
Formula Method ◽  
Reflection Formula

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.

ISOTROPY OF THE ZERO-POINT FIELD IN A UNIFORMLY ACCELERATED FRAME

1989 ◽  
Vol 04 (28) ◽  
pp. 2719-2722
Author(s):  
G.W. KANG ◽  
J.K. SEO ◽  
J.H. YEE
Keyword(s):  
Scalar Field ◽  
Angular Dependence ◽  
Zero Point ◽  
Field Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Point Field

The angular dependence of the zero-point field energy of the massless scalar field in a uniformly accelerated frame is computed. The spectrum seen by the observer in the accelerated frame is shown to be isotropic and thus to be thermal.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

scholarly journals Modulation of optical absorption in m-Fe1−xRuxS2 and exploring stability in new m-RuS2

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Joshi ◽  
M. Ram ◽  
N. Limbu ◽  
D. P. Rai ◽  
B. Thapa ◽  
...  
Keyword(s):  
Optical Absorption ◽  
Phonon Dispersion ◽  
Applied Pressure ◽  
Orthorhombic Phase ◽  
Zero Point ◽  
Computational Method ◽  
Crystal Field Theory ◽  
Point Energy ◽  
Practical Applications ◽  
New Phase

AbstractA first-principle computational method has been used to investigate the effects of Ru dopants on the electronic and optical absorption properties of marcasite FeS2. In addition, we have also revealed a new marcasite phase in RuS2, unlike most studied pyrite structures. The new phase has fulfilled all the necessary criteria of structural stability and its practical existence. The transition pressure of 8 GPa drives the structural change from pyrite to orthorhombic phase in RuS2. From the thermodynamical calculation, we have reported the stability of new-phase under various ranges of applied pressure and temperature. Further, from the results of phonon dispersion calculated at Zero Point Energy, pyrite structure exhibits ground state stability and the marcasite phase has all modes of frequencies positive. The newly proposed phase is a semiconductor with a band gap comparable to its pyrite counterpart but vary in optical absorption by around 106 cm−1. The various Ru doped structures have also shown similar optical absorption spectra in the same order of magnitude. We have used crystal field theory to explain high optical absorption which is due to the involvement of different electronic states in formation of electronic and optical band gaps. Lӧwdin charge analysis is used over the customarily Mulliken charges to predict 89% of covalence in the compound. Our results indicate the importance of new phase to enhance the efficiency of photovoltaic materials for practical applications.

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