Investigation of the Models of Magnetic Dendrimers by the Wang–Landau Method

Physics of the Solid State - The thermodynamic properties of the models of magnetic dendrimers were studied by the Monte Carlo method. The system state density is calculated; the ground state...     

A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background by Means of Conformal Mappings

A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under the algebra can be brought back to the general Natanzon hypergeometric potentials.     

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

Global Existence of Classical Solutions to the Fokker-Planck-BGK Equation

A kinetic model of the Fokker-Planck-Boltzmann equation is introduced by replacing the original Boltzmann collision operator with the Bhatnagar-Gross-Krook collision model (BGK collision model). This model equation, which we call the Fokker-Planck-BGK equation, has many physical features that the Fokker-Planck-Boltzmann equation possesses. We first establish an L ^∞ existence result for this equation, by which we construct the approximate solutions. Then, by means of the regularizing effects of the linear Fokker-Planck operator and L ^p estimates of local Maxwellians, we obtain some uniform estimates of the approximate solutions. Finally, combining those estimates and regularizing effects, we prove by a compactness argument that the equation has a global classical solution under rather general initial conditions. Supported by the Scientific Research Foundation of Huazhong University of Science and Technology (HUST-SRF).     

Scenario of Inflationary Cosmology from the Phenomenological Λ Models

Choosing the three phenomenological models of the dynamical cosmological term Λ, viz., , and Λ∼ρ where a is the cosmic scale factor, it has been shown by the method of numerical analysis for the considered non-linear differential equations that the three models are equivalent for the flat Universe k=0 and for arbitrary non-linear equation of state. The evolution plots for dynamical cosmological term Λ vs. time t and also the cosmic scale factor a vs. t are drawn here for k=0,+1. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.     

Targeting of Kolmogorov-Arnold-Moser Orbits by the Bailout Embedding Method in Two Coupled Standard Maps

A bailout embedding method for controlling chaos can make the chaotic orbits targeting into Kolmogorov- Arnold-Moser orbits. We apply this method to a high-dimensional system with two coupled standard maps. The numerical simulation shows that this method could obtain target islands in order and hence could be used to control chaos. Moreover, it is robust in the presence of weak external noise.     

Evolution of Bouncing Cosmological Models Due to the Self-Gravitational Corrections

A four-dimensional timelike brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. The self-gravitational corrections to the first Friedmann equation act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role. In a previous related paper (Setare in Eur. Phys. J. C 47:851, [2006]), bouncing cosmology was studied, from a holographic perspective, for the very special case of a brane that is void of any intrinsic matter sources. In this paper we extend the results of (Setare in Eur. Phys. J. C 47:851, [2006]). We consider the physically relevant case in which a perfect fluid with equation of state of radiation is present on the brane. Then, we describe solutions of the braneworld theory under investigation and also determine their stability. Specifically, if we do not consider the self-gravitational corrections, the AdS black hole with zero ADM mass, and open horizon is an attractor, while, if we consider, the AdS black hole with zero ADM mass and flat horizon, and D3-brane with non-zero energy density is a repeller.     

Comparison of the Parallel Tempering Algorithm and Multicanonical Method as Applied to Coarse-Grained Off-lattice Models for Folding Heteropolymers

We have performed Parallel Tempering simulations of hydrophobic-hydrophilic heteropolymers with a simple effective, coarse-grained off-lattice model with the selected monomers and compare the global energy minimums found with Parallel Tempering algorithm with the lowest energy states identified within the multicanonical algorithm.     

Canonical Quantization of Field Theories with Boundaries

The problem of canonical quantization of singular systems in a finite volume is studied by analysing a non-relativistic field theory. Firstly, we take the boundary conditions (BCs) as primary Dirac constraints. The quantization is performed canonically using Dirac’s procedure. Then, we quantize this model canonically in the classical solution space. We show that these two different quantization schemes are equivalent although they start from different settings.     

Green’s Function of the Schrödinger Equation in the Potential Quantization Method

Journal of Experimental and Theoretical Physics - The problem for determining Green’s function G(r, r') for the time-independent Schrödinger equation is considered using the...     

Renormalizability of a quark–gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark–gluon model with soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

Can the Pruned-Enriched Method be Used for the Simulation of Fluids?

The flat histogram version of pruned and enriched Rosenbluth method (FLATPERM) is an effective Monte Carlo method for calculating densities of states of polymers on a lattice. In this paper we generalize this method to calculate the densities of states of off-lattice systems. To demonstrate the feasibility of the approach, we perform sample calculations for the Lennard-Jones fluids. The densities of states of Lennard-Jones fluids simulated by Pruned-enriched method, i.e., the generalization of FLATPERM, agree with the densities simulated by Wang-Landau method in the range of high potential energy. However the direct extension of FLATPERM fails at low energy and a useful extension still needs to be found.     

Control of Semiquantum Chaos by the Nonfeedback Method

We numerically study the dynamic behaviour of coupled chaotic oscillators in a so-called semiquantum chaotic system in which one is classical and the other is quantum mechanical.Fourier spectra of the classical oscillator and the ground-state wavefunction of the quantum part have been investigated,when small pulse perturbations are applied.It is found that semiquantum chaos can also be successfully controlled by the nonfeedback method.     

A Note on the Extrinsic Phase Space Path Integral Method for Quantization on Riemannian Manifold Particle Motions — An Application of the Nash Embedding Theorem

We use Nash embedding for Riemann smooth manifolds to propose a constrained phase space path integral for quantization of one particle motion in a Riemannian manifold.     

An Efficient Approach for the Calculation of Nuclear Overlap Integrals by Means of Binomial Coefficients and Its Application

This paper examines the computational efficiency of the method of evaluating nuclear overlap integrals commonly encountered in nuclear reactions. As will be seen, the present formulation yields compact closed-form expressions which will make the calculation of nuclear overlap integrals easy. For practical applications, the computational technique used must be amenable to rapid evaluation and yield an acceptable degree of accuracy. Finally, the ratios for the non-Borromean two-nucleon halo systems are calculated by using new formulas which are important for the reaction analyses. The results of this calculation have been compared with those obtained according to one of the theoretical articles (Timofeyuk et al., Phys. Rev. C 68:021601(R), 2003). The same numerical results are presented for significant examples and they are briefly discussed.     

Solution of the Crow-Kimura and Eigen Models for Alphabets of Arbitrary Size by Schwinger Spin Coherent States

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an h-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary h and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler’s theorem for homogeneous functions is used to derive this ‘thermodynamic’ formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine h=2 alphabet and the nucleic acid h=4 alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the h=4 and h=20 cases. We also derive the maximum principle for the Eigen model for general h. The general result for the Eigen model reduces to a known result for h=2. Examples are presented for the nucleic acid h=4 and the amino acid h=20 alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.     

Exact Solutions of the Klein-Gordon Equation for the Scarf-Type Potential via Nikiforov-Uvarov Method

In this paper we present the exact solutions of the one-dimensional Klein-Gordon equation for the Scarf-type potential with equal scalar and vector potentials. Exact solutions and corresponding energy eigenvalues equation are obtained using Nikiforov-Uvarov mathematical method for the s-wave bound state. The PT-symmetry and Hermiticity for this potential are also considered. It will be shown that the obtained results of the Scarf-type potential are reduced to the results of the well-known potentials in the special cases.     

Bohmian Mechanics,the Quantum-Classical Correspondence and the Classical Limit: The Case of the Square Billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.