ZERO-POINT ENERGY OF A DILUTE DIELECTRIC BALL IN THE MODE SUMMATION METHOD

In the (ε1-ε2)2-approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a closed form the sum over the angular momentum before the integration over the imaginary frequencies. The linear in (ε1-ε2)2 contribution into the vacuum energy is removed by an appropriate subtraction. The role of the contact terms used in other approaches to this problem is elucidated.

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On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

10.26434/chemrxiv.8870594.v2 ◽

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>

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A NOTE ON THE CASIMIR ENERGY OF A MASSIVE SCALAR FIELD IN POSITIVE CURVATURE SPACE

Modern Physics Letters A ◽

10.1142/s0217732304012836 ◽

2004 ◽

Vol 19 (02) ◽

pp. 111-116 ◽

Cited By ~ 17

Author(s):

E. ELIZALDE ◽

A. C. TORT

Keyword(s):

High Temperature ◽

Scalar Field ◽

Zeta Function ◽

Vacuum Energy ◽

Positive Curvature ◽

Zero Point ◽

Casimir Energy ◽

Massive Scalar ◽

Zero Temperature ◽

Massive Scalar Field

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in R1×S3 space, allowing also for deviations from the standard conformal value ξ=1/6, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. The analytic continuation can be performed in two ways, which are seen to be equivalent.

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Shadows of trans-Planckian physics on cosmology and the role of the zero-point energy density

Physical Review D ◽

10.1103/physrevd.82.043519 ◽

2010 ◽

Vol 82 (4) ◽

Cited By ~ 7

Author(s):

Gianpiero Mangano

Keyword(s):

Energy Density ◽

Zero Point ◽

Zero Point Energy ◽

Point Energy

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CASIMIR ENERGY OF A DILUTE DIELECTRIC BALL AT ZERO AND FINITE TEMPERATURE

International Journal of Modern Physics A ◽

10.1142/s0217751x02010121 ◽

2002 ◽

Vol 17 (06n07) ◽

pp. 790-793 ◽

Cited By ~ 5

Author(s):

V. V. NESTERENKO ◽

G. LAMBIASE ◽

G. SCARPETTA

Keyword(s):

Free Energy ◽

Electromagnetic Field ◽

Angular Momentum ◽

High Temperature ◽

Finite Temperature ◽

Bessel Functions ◽

Thermodynamic Characteristics ◽

Casimir Energy ◽

Addition Theorem ◽

Temperature Expansion

The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated. The T3-term in the low temperature expansion of the free energy is recovered (this term has been lost in our previous calculations).

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Thermodynamic Stability of Ice II and Its Hydrogen-Disordered Counterpart: Role of Zero-Point Energy

The Journal of Physical Chemistry B ◽

10.1021/acs.jpcb.5b09544 ◽

2015 ◽

Vol 120 (8) ◽

pp. 1843-1848 ◽

Cited By ~ 11

Author(s):

Tatsuya Nakamura ◽

Masakazu Matsumoto ◽

Takuma Yagasaki ◽

Hideki Tanaka

Keyword(s):

Thermodynamic Stability ◽

Zero Point ◽

Zero Point Energy ◽

Point Energy

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Riemann zeta zeros and zero-point energy

International Journal of Modern Physics A ◽

10.1142/s0217751x14500511 ◽

2014 ◽

Vol 29 (09) ◽

pp. 1450051 ◽

Cited By ~ 4

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.

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Dark energy and dark matter as due to zero point energy

Journal of Plasma Physics ◽

10.1017/s0022377812001055 ◽

2012 ◽

Vol 79 (3) ◽

pp. 327-334 ◽

Cited By ~ 5

Author(s):

BO LEHNERT

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Energy Density ◽

Vacuum Energy ◽

Mass Density ◽

Zero Point ◽

Vacuum Energy Density ◽

Zero Point Energy ◽

Observable Universe ◽

Point Energy

AbstractAn attempt is made to explain dark energy and dark matter of the expanding universe in terms of the zero point vacuum energy. This analysis is mainly limited to later stages of an observable nearly flat universe. It is based on a revised formulation of the spectral distribution of the zero point energy, for an ensemble in a defined statistical equilibrium having finite total energy density. The steady and dynamic states are studied for a spherical cloud of zero point energy photons. The ‘antigravitational’ force due to its pressure gradient then represents dark energy, and its gravitational force due to the energy density represents dark matter. Four fundamental results come out of the theory. First, the lack of emitted radiation becomes reconcilable with the concepts of dark energy and dark matter. Second, the crucial coincidence problem of equal orders of magnitude of mass density and vacuum energy density cannot be explained by the cosmological constant, but is resolved by the present variable concepts, which originate from the same photon gas balance. Third, the present approach becomes reconcilable with cosmical dimensions and with the radius of the observable universe. Fourth, the deduced acceleration of the expansion agrees with the observed one. In addition, mass polarity of a generalized gravitation law for matter and antimatter is proposed as a source of dark flow.

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