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Phonon quasi-particles have been monumental in microscopically understanding thermodynamics and transport properties in condensed matter for decades. Phonons have one-to-one correspondence with harmonic eigenstates and their energies are…
The polariton system is studied by a concise approach using a simple model. A new ground state with negative energy is obtained and found to exhibit the symmetry breaking.
We obtain an analytic solution for a three-parameter class of logarithmic potentials at zero energy. The potential terms are products of the inverse square and the inverse log to powers 2, 1 and 0. The configuration space is the…
The topological sigma model with the semi-infinite cigar-like target space (black hole geometry) is considered. The model is shown to possess unsuppressed instantons. The noncompactness of the moduli space of these instantons is responsible…
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a characterization of the smooth potential energy functions on the…
Vortex states of photons, electrons, and other particles are non--plane-wave solutions of the corresponding wave equation with helicoidal wave fronts. These states possess an intrinsic orbital angular momentum with respect to the average…
The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory…
Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support…
We study numerically gravitational collapse of a spherically symmetric instanton particle in five dimensions. We show that the late stages of the process are characterized by a nearly constant ``free energy'', the value of which matches…
A new supersymmetry method for the generation of the quasi-exactly solvable (QES) potentials with two known eigenstates is proposed. Using this method we obtained new QES potentials for which we found in explicit form the energy levels and…
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among…
Nonsingular black holes have received much attention in recent years as they provide an opportunity to avoid the singularities inherent to the mathematical black holes predicted by general relativity. Based on the assumption that…
The program to construct minimum-uncertainty coherent states for general potentials works transparently with solvable analytic potentials. However, when an analytic potential is not completely solvable, like for a double-well or the linear…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
We discuss the conditions under which static, finite-energy, configurations of a complex scalar field $\phi$ with constant phase and spherically symmetric norm exist in a potential of the form $V(\phi^*\phi, \phi^N+\phi^{*N})$ with…
We analyze the zero energy solutions, of a two dimensional system which undergoes a non-radial symmetric, complex potential V(r,$\phi$). By virtue of the coherent states concept, the localized states are constructed, and the consequences of…
We define a minimal model with Universal Extra Dimensions, and begin to study its phenomenology. The collider signals of the first KK level are surprisingly similar to those of a supersymmetric model with a nearly degenerate superpartner…
An octopus program is demonstrated to generate electron energy levels in three-dimensional geometrical potential wells. The wells are modeled to have shapes similar to cone, pyramid and truncated-pyramid. To simulate the electron energy…
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 one space dimension. In particular we compute the vacuum…
In spite of its rather weird properties which include violation of the dominant-energy condition, the requirement of superluminal sound speed and increasing vacuum-energy density, phantom energy has recently attracted a lot of scientific…