Jose Perico Esguerra

Exact moments in a continuous time random walk with complete memory of its history.

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.

Bound states for multiple Dirac-δ wells in space-fractional quantum mechanics

Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength −g (g > 0), in the space-fractional Schrodinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Foxs H-function.

Brownian motion of a charged particle driven internally by correlated noise.

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that the speed of a free particle and the magnitude of the acceleration of a particle in a linear potential have larger values compared to the non-minimal length counterparts - the increase in magnitudes come from multiplicative factors proportional to what is known as the generalized uncertainty principle parameter. Our analysis of oscillator systems suggests that the characteristic frequencies of systems also have larger values than the non-minimal length counterparts. In connection with this, we discuss a kind of experimental test with which the existence of a minimal length may be detected on a classical level.

Periods of relativistic oscillators with even polynomial potentials

Abstract The authors modify a non-perturbative variational approach based on the Principle of Minimal Sensitivity to calculate the periods of relativistic oscillators with even polynomial potentials. The optimization of the variational parameter is adapted by introducing additional free parameters whose values are set using the ultrarelativistic limit of the period as a boundary condition. Compact general approximations for the potentials x 2 2 + x 2 m 2 m , ∑ n = 1 m x 2 n 2 n and x 2 m 2 m prove to be accurate over the whole solution domain and even for large values of m.

Evolution of ideal gas mixtures confined in an insulated container by two identical pistons

We study the quasistatic adiabatic expansion of monatomic-diatomic ideal gas mixtures bounded by identical pistons and obtain closed form expressions for the temperature of the gas as a function of the time. We find that the temperature decreases as an inverse power of the time for large times, with the exponent as a function of the monatomic to diatomic gas ratio. The piston speeds increase from zero to a maximum value determined by the heat capacity of the gas and the masses of the pistons. Plots of the temperature and piston speed versus the logarithm of the time show points of inflection, which are interpreted as signaling the onset of steady state behavior. These points shift to later times as the monatomic to diatomic gas ratio is varied from purely monatomic to purely diatomic.

Wind-influenced projectile motion

We solved the wind-influenced projectile motion problem with the same initial and final heights and obtained exact analytical expressions for the shape of the trajectory, range, maximum height, time of flight, time of ascent, and time of descent with the help of the Lambert W function. It turns out that the range and maximum horizontal displacement are not always equal. When launched at a critical angle, the projectile will return to its starting position. It turns out that a launch angle of 90° maximizes the time of flight, time of ascent, time of descent, and maximum height and that the launch angle corresponding to maximum range can be obtained by solving a transcendental equation. Finally, we expressed in a parametric equation the locus of points corresponding to maximum heights for projectiles launched from the ground with the same initial speed in all directions. We used the results to estimate how much a moderate wind can modify a golf ball’s range and suggested other possible applications.

Euclidean path integral formalism in deformed space with minimum measurable length

We study time-evolution at the quantum level by developing the Euclidean path-integral approach for the general case where there exists a minimum measurable length. We derive an expression for the momentum-space propagator which turns out to be consistent with recently developed β-canonical transformation. We also construct the propagator for maximal localization which corresponds to the amplitude that a state which is maximally localized at location ξ′ propagates to a state which is maximally localized at location ξ″ in a given time. Our expression for the momentum-space propagator and the propagator for maximal localization is valid for any form of time-independent Hamiltonian. The nonrelativistic free particle, particle in a linear potential, and the harmonic oscillator are discussed as examples.

Lattice gauge theory and gluon color-confinement in curved spacetime

The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman–Robertson–Walker (FRW) metric. Last, we discussed possible future numerical implementation of lattice QCD in curved spacetime.

A Poisson-like closed-form expression for the steady-state wealth distribution in a kinetic model of gambling

An approximate but closed-form expression for a Poisson-like steady state wealth distribution in a kinetic model of gambling was formulated from a finite number of its moments, which were generated from a βa,b(x) exchange distribution. The obtained steady-state wealth distributions have tails which are qualitatively similar to those observed in actual wealth distributions.