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Communications in Theoretical Physics

Relativistic Quantum Statistical Aharonov-Bohm Effect of Many-Boson System in Mesoscopic Ring

Zhao Hongkang

Published Jan 30, 1998• 2 citations
Publisher

Abstract

The relativistic quantum statistical properties of charged many-boson system with rest mass for each boson confined in a mesoscopic ring are investigated. The small ring is threaded by Aharonov–Bohm magnetic flux . At low temperature, , we have performed analytical calculations starting from evaluating the logarithm of grand partition function by using Mellin transform. The pair-production problem is excluded from our consideration for the temperature is low. The number density, total energy, specific heat and persistent current are obtained in general. These thermodynamic functions oscillate periodically in with period , and they are related to the modified Bessel functions of the second kind The chemical potential is restricted by to ensure the positive number density of particles and the convergence of fugacity expansions. We find that these functions decay exponentially with temperature, and they also decrease as the circumference L increases. The non-relativistic and ultra-relativistic behaviors of these functions are discussed by considering the asymptotic behaviors of . There is no Bose–Einstein condensation in this system.

DOI
10.1088/0253-6102/29/1/33

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The relativistic quantum statistical properties of charged many-boson system with rest mass for each boson confined in a mesoscopic ring are investigated. The small ring is threaded by Aharonov–Bohm magnetic flux . At low temperature, , we have performed analytical calculations starting from evaluating the logarithm of grand partition function by using Mellin transform. The pair-production problem is excluded from our consideration for the temperature is low. The number density, total energy, specific heat and persistent current are obtained in general. These thermodynamic functions oscillate periodically in with period , and they are related to the modified Bessel functions of the second kind The chemical potential is restricted by to ensure the positive number density of particles and the convergence of fugacity expansions. We find that these functions decay exponentially with temperature, and they also decrease as the circumference L increases. The non-relativistic and ultra-relativistic behaviors of these functions are discussed by considering the asymptotic behaviors of . There is no Bose–Einstein condensation in this system.
Based upon a tight-binding model Hamiltonian and by applying the Jordan-Wigner transformation, the Aharonov-Bohm (AB) effect for charged hard-core bosons in one-dimensional (1D) mesoscopic rings is investigated for the first time. By introducing a specific unitary transformation, the energy spectrum and the persistent charge current are analytically derived for ID perfect lattices. Similar to electron systems, it has been found that the energy and persistent current are periodic in AB flux with the period Φ0=hc/q. More interestingly, we have exactly shown that, in the absence of the external AB flux, the charge current can be self-sustained via the AB effect, which is in fact the ground state of the system regardless of the number of hard-core bosons being even or odd.
To study the manifestation of the Aharonov-Bohm effect in many-body systems we consider the statistical mechanics of the Gross-Neveu model on a ring (1+1 dimensions) and on a cylinder (2+1 dimensions) with a thin solenoid coinciding with the axis. For such systems with a non-trivial magnetic flux (θθθ) many thermodynamical observables, such as the order parameter, induced current and virial coefficients, display periodic but non-analytic dependence on θθθ. In the 2+1 dimensional case we further find that there is an interval of θ∈(1/3,2/3)θ\in(1/3,2/3)θ∈(1/3,2/3) (modulo integers) where parity is always spontaneously broken, independent of the circumference of the cylinder. We show that the mean-field character of the phase transitions is preserved to the leading order in 1/N1/N1/N, by verifying the θθθ-independence of all the critical exponents. The precise nature of the quasi-particle, locally fermion-like and globally anyon-like, is illuminated through the calculation of the equal-time commutator and the decomposition of the propagator into a sum over paths classified by winding numbers.
We perform analytical calculations to study the persistent current I of a q-charged hard-core boson gas in mesoscopic rings enclosing a magnetic flux \ensuremath{\Phi}, and find that this current is periodic in \ensuremath{\Phi} with the period ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/q. More interestingly, in the presence of a single \ensuremath{\delta}-function impurity, it has been found that there generally exists a spontaneous Aharonov-Bohm flux as long as the current-induced flux is included.
Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions to statistical mechanics, condensed matter, and, more recently, quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable of capturing important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a type of Aharonov-Bohm effect that goes beyond the particlelike effect, reflecting the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics. Published by the American Physical Society 2024
Statistical properties of an ideal gas of relativistic fermions trapped in a D-dimensional power-law potential are studied, in which the effect of particle–antiparticle pair production is taken into account. It is shown that the relativistic effect is considerable even at very low temperatures for the system with Fermi energy comparable with the rest energy of a particle. In contrast, the effect of pair production is significant at high temperatures, but negligible at low temperatures. Moreover, it is found that the pair production results in several novel characteristics, such as the asymptotic behavior of chemical potential and rapid increase of heat capacity in the high temperature region.
Persistent charge and spin currents due to Aharonov - Bohm and Aharonov - Casher interferences of correlated electrons moving along a mesoscopic ring are discussed at finite temperature. As a function of applied flux the ground-state persistent currents have the shape of a generalized saw-tooth, i.e. they consist of piecewise straight segments. The periods and amplitudes of the oscillations are associated with the properties of the Fermi surface of the elementary excitations (two Dirac seas), namely the group velocities and the matrix of dressed generalized charges (Luttinger parameters). The temperature reduces the amplitudes of oscillation by smearing the Fermi surface in a similar way to that for the de Haas - van Alphen effect in 3D metals. The amplitude of higher harmonics decreases more quickly with T than the fundamental one, changing the saw-tooth to a more sinusoidal form with much smaller amplitude. The controlling parameters are the ratios of the thermal energy to the level spacings in the ring. The results are discussed in the context of the exact Bethe ansatz solutions for the Hubbard chain and the supersymmetric t - J model.