Related papers: Phase Transition in the Number Partitioning Proble…
Parametric representations of the high-density nuclear equation of state are used in constructing models for interpreting the astrophysical observations of neutron stars. This study explores how accurately equations of state with strong…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…
Lipkin model of arbitrary particle-number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunneling. Our new…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…
Classical escape in 2D Hamiltonian systems with the mixed state has been studied numerically and analytically. The wide class of potentials with the mixed state is presented by polinomial potentials. In potentials, where the mixed state…
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
When a quantum state traverses a path, while being under the influence of a gauge potential, it acquires a geometric phase that is often more than just a scalar quantity. The variety of unitary transformations that can be realised by this…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods.…
The number partitioning problem can be interpreted physically in terms of a thermally isolated non-interacting Bose gas trapped in a one-dimensional harmonic oscillator potential. We exploit this analogy to characterize, by means of a…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
The following is a thermodynamic analysis of a III order (and some aspects of a IV order) phase transition. Such a transition can occur in a superconductor if the normal state is a diamagnet. The equation for a phase boundary in an H-T (H…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that…
Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the…