One-dimensional Periodic Potential Research Articles

Phase synchronization for two Brownian motors with bistable coupling on a ratchet

We study phase synchronization for a walker on a ratchet potential. The walker consist of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization.

Magnetotransport in a periodically modulated graphene monolayer

Motivated by the realization that periodic ripples in suspended graphene can result in a periodic potential, which can also be induced by interaction with a substrate, we have carried out a detailed investigation of the electrical transport properties of a graphene monolayer which is modulated by a weak one-dimensional periodic potential in the presence of a perpendicular magnetic field $(B)$. The periodic modulation broadens the Landau Levels into bands which oscillate with $B$. The electronic conduction in this system can take place through either diffusive scattering or collisional scattering off impurities. Both these contributions to electronic transport are taken into account in this work. In addition to the appearance of commensurability oscillations in both the collisional and diffusive contributions, we find that Hall resistance also exhibits commensurability oscillations. Furthermore, the period and amplitude of these commensurability oscillations in the transport parameters and the effect of temperature on them are also discussed in this work.

Cooperative jump motions of jammed particles in a one-dimensional periodic potential

Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated and it is compared with theoretical estimates. We find that the size distribution of the cooperative jump motions obeys an exponential law in a large system.

Ratchet Effects Induced by Terahertz Radiation in Heterostructures with a Lateral Periodic Potential

We report on the observation of the Seebeck ratchet effect. The effect is measured in semiconductor heterostructures with a one-dimensional lateral potential excited by terahertz radiation. The photocurrent generation is based on the combined action of a spatially periodic in-plane potential and a spatially modulated light, which gives rise to a modulation of the local temperature. In addition to the polarization-independent current due to the Seebeck ratchet effect, we observe a photon helicity dependent response and propose a microscopic mechanism to interpret the experimental findings.

Conduction bands in classical periodic potentials

The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time to perform the measurement. This paper considers the possibility that ΔE, the uncertainty in the energy, may be complex. To understand the effect of a particle having a complex energy, the behaviour of a classical particle in a one-dimensional periodic potential V(x) = −cos(x) is studied. On the basis of detailed numerical simulations it is shown that if the energy of such a particle is allowed to be complex, the classical motion of the particle can exhibit two qualitatively different behaviours: (i) The particle may hop from classically allowed site to nearest-neighbour classically allowed site in the potential, behaving as if it were a quantum particle in an energy gap and undergoing repeated tunnelling processes or (ii) the particle may behave as a quantum particle in a conduction band and drift at a constant average velocity through the potential as if it were undergoing resonant tunnelling. The classical conduction bands for this potential are determined numerically with high precision.

Landau Levels and Quantum Hall Effect in Graphene Superlattices

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling become 4(2N + 1)-fold degenerate (with N = 0, 1, 2, ..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity sigma_{xy} showing a step of size 4(2N + 1)e;{2}/h. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.

Ground-state properties of a Tonks-Girardeau gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.

Excitations of Bose-Einstein condensates in a one-dimensional periodic potential

We report on the experimental investigation of the response of a three-dimensional Bose-Einstein condensate (BEC) in the presence of a one-dimensional (1D) optical lattice. By means of Bragg spectroscopy we probe the band structure of the excitation spectrum in the presence of the periodic potential. We selectively induce elementary excitations of the BEC choosing the transferred momentum and we observe different resonances in the energy transfer, corresponding to the transitions to different bands. The frequency, the width and the strength of these resonances are investigated as a function of the amplitude of the 1D optical lattice.

Noise-induced transport in a rough ratchet potential

Several years ago Zwanzig considered the diffusion in a potential that is spatially rough due to hierarchical structure of protein. We extend this idea to the overdamped Brownian dynamics in a one-dimensional periodic and rough ratchet potential. A general expression is obtained for the effective current at the steady state. Variation in both current and efficiency has been studied with respect to the amplitude of the roughness and an external nonequilibrium, nonthermal driving force. It has been shown that roughness hinders current quite significantly. Our analysis is corroborated by detailed numerical simulations and may be useful in the context of laser switching of current through molecular wires.

Comparing the image potentials for intercalated graphene with a two-dimensional electron gas with and without a gated grating

We calculate the surface response function and the image potential of a system of layered two-dimensional (2D) electron gas structures. A point charge is placed at a distance away from the surface which lies in the $xy$- plane. These 2D layers are coupled through the Coulomb interaction and there is no interlayer electron hopping. The separation between adjacent layers can be adjusted to investigate the roles which the layer separation and the number of layers play on both the surface response function and the image potential. Specifically, we consider the system composed of graphene layers or the layered 2D electron gas (EG) formed at the interface of a semiconductor heterostructure such as GaAs/AlGaAs. We show that the image potential for graphene is qualitatively the same as for the 2DEG. We examine the way in which the image potential is modified by applying a one-dimensional periodic electrostatic potential (through a gated grating for modulation). The results indicate that the charge screening for graphene is not much different from the 2DEG.

Fermionic superfluid properties in a one-dimensional optical lattice

We discuss various superfluid properties of a two-component Fermi system in the presence of a tight one-dimensional periodic potential in a three-dimensional system. We use zero temperature mean field theory and derive analytical expressions for the Josephson current, the sound velocity, and the center-of-mass oscillations in the Bardeen, Cooper, and Schrieffer-Bose Einstein condensation (BCS-BEC) crossover region.

Equation of state and effective mass of the unitary Fermi gas in a one-dimensional periodic potential

By solving the Bogoliubov--de Gennes equations at zero temperature, we study the effects of a one-dimensional optical lattice on the behavior of a superfluid Fermi gas at unitarity. We show that, due to the lattice, at low densities the gas becomes highly compressible and the effective mass is large, with a consequent significant reduction of the sound velocity. We discuss the role played by the lattice in the formation of molecules and the emergence of two-dimensional effects in the equation of state. Predictions for the density profiles and for the frequency of the collective oscillations in the presence of harmonic trapping are also given.

Smoluchowski equation approach for quantum Brownian motion in a tilted periodic potential

Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski equation already proposed-viz., J. Ankerhold [Phys. Rev. Lett. 87, 086802 (2001)] and W. T. Coffey [J. Phys. A 40, F91 (2007)]-are compared in detail in a particular application to the dynamics of a point Josephson junction. Various characteristics (stationary distribution, current-voltage characteristics, mean first passage time, linear ac response) are evaluated via continued fractions and finite integral representations in the manner customarily used for the classical Smoluchowski equation. The deviations from the classical behavior, discernible in the dc current-voltage characteristics as enhanced current for a given voltage and in the resonant peak in the impedance curve as an enhancement of the Q factor, are, respectively, a manifestation of relatively high-temperature nondissipative tunneling (reducing the barrier height) and dissipative tunneling (reducing the damping of the Josephson oscillations) near the top of a barrier.

Electron Beam Supercollimation in Graphene Superlattices

Although electrons and photons are intrinsically different, importing useful concepts in optics to electronics performing similar functions has been actively pursued over the last two decades. In particular, collimation of an electron beam is a long-standing goal. We show that ballistic propagation of an electron beam with virtual no spatial spreading or diffraction, without a waveguide or external magnetic field, can be achieved in graphene under an appropriate class of experimentally feasible one-dimensional external periodic potentials. The novel chiral quasi-one-dimensional metallic state that the charge carriers are in originates from a collapse of the intrinsic helical nature of the charge carriers in graphene owing to the superlattice potential. Beyond providing a new way to constructing chiral one-dimensional states in two dimensions, our findings should be useful in graphene-based electronic devices (e.g., for information processing) utilizing some of the highly developed concepts in optics.

Two-particle states in the Hubbard model

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with an attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.

Single-particle excitations in periodically modulated two-dimensional electron gas

A theoretical investigation is made of the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional periodic potential. We embark on the single-particle excitations within a two-subband model in the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe the existence of interesting esthetic necktie gaps that are found to center at the zone boundaries within the intersubband single-particle excitations. We discuss the dependence of the size of necktie gaps on the modulation potential.

Dirac and Klein-Gordon particles in one-dimensional periodic potentials

We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic potential. For massless fermions the dispersion relation shows a zero gap for carriers with zero momentum in the direction parallel to the barriers in agreement with the well-known "Klein paradox". Numerical results for the energy spectrum and the density of states are presented. Those for fermions are appropriate to graphene in which carriers behave relativistically with the "light speed" replaced by the Fermi velocity. In addition, we evaluate the transmission through a finite number of barriers for fermions and zero-spin bosons and relate it with that through a superlattice.

Directed transport of Brownian particles in a changing temperature field

We study the interaction of Brownian particles with a changing temperature field in the presence of a one-dimensional periodic adiabatic potential. We show the existence of directed transport through the determination of the overall current of Brownian particles crossing the boundary of the system. With respect to the case of Brownian particles in a thermal bath, we determine a current which exhibits a contribution explicitly related to the presence of a thermal gradient. Beyond the self-consistent calculation of the temperature and probability density distribution of Brownian particles, we evaluate the energy consumption for directed transport to take place. Our description is based on Streater's model, and solutions are obtained by perturbing the system from its initial thermodynamic equilibrium state.

Entropy versus energy: The phase behavior of a hard-disk mixture in a periodic external potential

The phase behavior of a 50% binary hard-disk mixture with diameter ratio sigmaB/sigmaA=0.414 , which is exposed to a one-dimensional periodic potential, is examined via Monte Carlo simulations. We find an induced structural crossover in the modulated liquid. At higher densities, depending on the strength of the external potential, the system exhibits a tunable demixing transition, followed by fluid-solid coexistence of an equimolar mixture with the S1(AB) square lattice. We find a decoupled melting of the sublattices of the S1(AB) lattice. The melting of the small-component sublattice perpendicular to the external potential minima leads to fissuring in the large-component sublattice.

Phase transitions in two-dimensional model colloids in a one-dimensional external potential

Two-dimensional melting transitions for model colloids in the presence of a one-dimensional external periodic potential are investigated using Monte Carlo simulation and finite size scaling techniques. Here we explore a hard disk system with commensurability ratio p=sqrt[3]as/(2d)=2, where as is the mean distance between the disks and d the period of the external potential. Three phases, the modulate liquid, the locked smectic, and the locked floating solid are observed, in agreement with other experimental and analytical studies. Various statistical quantities like order parameters, their cumulants, and response functions, are used to obtain a phase diagram for the transitions between these three phases.