Preheating with fractional powers

We consider preheating in models in which the potential for the inflaton is given by a fractional power, as is the case in axion monodromy inflation. We assume a standard coupling between the inflaton field and a scalar matter field. We find that in spite of the fact that the oscillation of the inflaton about the field value which minimizes the potential is anharmonic, there is nevertheless a parametric resonance instability, and we determine the Floquet exponent which describes this instability as a function of the parameters of the inflaton potential.

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The Casimir effect with quantized charged scalar matter in background magnetic field

International Journal of Modern Physics A ◽

10.1142/s0217751x14500523 ◽

2014 ◽

Vol 29 (09) ◽

pp. 1450052 ◽

Cited By ~ 3

Author(s):

Yu. A. Sitenko ◽

S. A. Yushchenko

Keyword(s):

Magnetic Field ◽

Boundary Condition ◽

Boundary Conditions ◽

Casimir Force ◽

Matter Field ◽

Particle Energy ◽

Parallel Plates ◽

Charged Scalar ◽

Scalar Matter ◽

Background Magnetic Field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the operator of one-particle energy squared be self-adjoint and positive-definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates.

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FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE

International Journal of Mathematics ◽

10.1142/s0129167x07004102 ◽

2007 ◽

Vol 18 (03) ◽

pp. 281-299 ◽

Cited By ~ 36

Author(s):

VASILY E. TARASOV

Keyword(s):

Fourier Series ◽

Fractional Derivative ◽

Taylor Series ◽

Fractional Derivatives ◽

Fractional Power ◽

Weyl Quantization ◽

Fractional Powers ◽

Derivative Operator ◽

Quantization Procedure ◽

Definition Of

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

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On Gauge Invariant Cosmological Perturbations in UV-modified Hořava Gravity: A Brief Introduction

EPJ Web of Conferences ◽

10.1051/epjconf/201816808003 ◽

2018 ◽

Vol 168 ◽

pp. 08003 ◽

Cited By ~ 1

Author(s):

Mu-In Park

Keyword(s):

Detailed Balance ◽

Big Bang ◽

Matter Field ◽

Cosmological Perturbations ◽

Scale Invariant ◽

Gauge Invariant ◽

Four Dimensions ◽

Detailed Balance Condition ◽

Scalar Matter ◽

Horava Gravity

We revisit gauge invariant cosmological perturbations in UV-modified, z = 3 Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. We confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology.

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CASIMIR ENERGY AND FORCE INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

International Journal of Modern Physics A ◽

10.1142/s0217751x13501613 ◽

2013 ◽

Vol 28 (31) ◽

pp. 1350161 ◽

Cited By ~ 3

Author(s):

VOLODYMYR M. GORKAVENKO ◽

YURII A. SITENKO ◽

OLEXANDER B. STEPANOV

Keyword(s):

Magnetic Flux ◽

Vacuum Polarization ◽

Dirichlet Boundary ◽

Topological Defect ◽

Casimir Energy ◽

Matter Field ◽

Tube Radius ◽

Finite Radius ◽

Polarization Effects ◽

Scalar Matter

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

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Fractional powers of operators defined on a Fréchet space

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500022264 ◽

1984 ◽

Vol 27 (2) ◽

pp. 165-180 ◽

Cited By ~ 5

Author(s):

W. Lamb

Keyword(s):

Banach Space ◽

Fractional Power ◽

Fréchet Space ◽

Frechet Space ◽

Fractional Powers ◽

Fractional Powers Of Operators ◽

Image Position ◽

Densely Defined

The problem of finding a suitable representation for a fractional power of an operator defined in a Banach space X has, in recent years, attracted much attention. In particular, Balakrishnan [1], Hovel and Westphal [3] and Komatsu [4] have examined the problem of defining the fractionalpower (–A)α for closed densely-defined operators A such that

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Induced vacuum current and magnetic field in the background of a vortex

International Journal of Modern Physics A ◽

10.1142/s0217751x16500172 ◽

2016 ◽

Vol 31 (06) ◽

pp. 1650017 ◽

Cited By ~ 2

Author(s):

Volodymyr M. Gorkavenko ◽

Iryna V. Ivanchenko ◽

Yurii A. Sitenko

Keyword(s):

Magnetic Field ◽

Side Surface ◽

Matter Field ◽

Transverse Size ◽

Compton Wavelength ◽

Charged Scalar ◽

Quantum Matter ◽

Scalar Matter ◽

Bohm Effect ◽

Aharonov Bohm

A topological defect in the form of the Abrikosov–Nielsen–Olesen vortex is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. Charged scalar matter field is quantized in the vortex background with the perfectly reflecting (Dirichlet) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex and a magnetic field directed along the vortex are induced in the vacuum, if the Compton wavelength of the matter field exceeds considerably the transverse size of the vortex. The vacuum current and magnetic field are periodic in the value of the gauge flux of the vortex, providing a quantum-field-theoretical manifestation of the Aharonov–Bohm effect. The total flux of the induced vacuum magnetic field attains notable finite values even for the Compton wavelength of the matter field exceeding the transverse size of the vortex by just three orders of magnitude.

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TIME IN THE CHAOTIC INFLATION MODEL AND NUMERICAL CALCULATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x95001121 ◽

1995 ◽

Vol 10 (16) ◽

pp. 2317-2332

Author(s):

YOSHIAKI OHKUWA ◽

TETSURO KITAZOE ◽

YOSHIHIKO MIZUMOTO

Keyword(s):

Quantum Gravity ◽

Perturbation Method ◽

Orbital Motion ◽

Semiclassical Approximation ◽

Natural Extension ◽

Matter Field ◽

Time Variable ◽

Inflation Model ◽

Scalar Matter ◽

Scalar Mass

The time variable is considered in the quantum gravity theory and calculated explicitly in the framework of the chaotic inflationary scenario where the scalar matter field has a contribution to the time variable in addition to the gravity field. The time formulated under the semiclassical approximation is a natural extension of that in the classical orbital motion. A perturbation method is introduced in terms of the scalar mass to obtain analytically solvable expressions for the time. The Wheeler-DeWitt equation is solved numerically to ensure that the semiclassical approximation is well justified. We examine the obtained time in detail and find that it is reasonable to consider it as time in the region where the semiclassical approximation is well justified.

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A Splitting Scheme to Solve an Equation for Fractional Powers of Elliptic Operators

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2015-0031 ◽

2016 ◽

Vol 16 (1) ◽

pp. 161-174 ◽

Cited By ~ 1

Author(s):

Petr N. Vabishchevich

Keyword(s):

Dirichlet Boundary ◽

Model Problem ◽

Fractional Power ◽

Dirichlet Boundary Conditions ◽

Splitting Scheme ◽

Fractional Powers ◽

Splitting Schemes ◽

Unconditionally Stable ◽

Spatial Variables ◽

Finite Difference Approximations

AbstractAn equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an auxiliary Cauchy problem for a pseudo-parabolic equation. Unconditionally stable vector-additive schemes (splitting schemes) are constructed. Numerical results for a model problem in a rectangle calculated using the splitting with respect to spatial variables are presented.

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