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When noninteracting fermions are confined in a $D$-dimensional region of volume $\mathrm{O}(L^D)$ and subjected to a continuous (or piecewise continuous) potential $V$ which decays sufficiently fast with distance, in the thermodynamic…
Static field classical configurations in (1+1)-dimensions for new non-linear potential models are investigated from an isospectral potential class and the concept of bosonic zero- mode solution. One of the models here considered has a…
We study the properties of a class of quantum field theories endowed with an equal number of anti commuting and commuting field variables, the most common example being the supersymmetric models. Based on the scaling properties of the…
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
For field theories in one time and one space dimensions we propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti--symmetric channels.…
In quantum theory the vacuum is defined as a state of minimum energy that is devoid of particles but still not completely empty. It is perhaps more surprising that its definition depends on the geometry of the system and on the trajectory…
Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical…
This work is mainly based on some theoretical surveys on two dimensional quantum gravitational well, considering harmonic oscillator potential causes an effective plank constant. We find that there is a similarity between two different…
There are few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states…
Let u be the equilibrium potential of a compact set K. An electrostatic skeleton of K is a positive measure whose closed support has connected complement and no interior, and whose potential is equal to u near infinity. We prove the…
We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a…
A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound…
Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of $|x|^\nu$ ($\nu>0$) type energies…
Inspired by the recent conjecture that black holes are condensates of gravitons, we investigate a simple model for the black hole degrees of freedom that is consistent both from the point of view of Quantum mechanics and of General…
In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than…
We propose the treatment of the lowest bound states near the vortex core on the basis of the self-adjoint extension of the Hamiltonian with the localized magnetic flux of Aaronov-Bohm type. It is shown that in the limit {\varkappa} >> 1 the…
We study the model of spherically symmetric and spatially homogeneous gravitational collapse of a minimally coupled scalar field. Our study focuses on obtaining the scalar field potential that leads to a final equilibrium state in the…
The ground state energy of a quantum field in the background of classical field configurations is considered. The subject of the ground state energy in framework of the quantum field theory is explained. The short review of calculation…
The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic…
It is known that there exist a limited number of analytic potentials with the unusual property that any bound quantum state therein will be periodic in time. This is known as a perfect quantum state revival. Examples of such potentials are…