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You-Quan Li

Publications and source records attributed to You-Quan Li.

89 records · Page 5Linked to original sources
arXiv2000

Commutation Relations in Mesoscopic Electric Circuits

In the talk, I briefly demonstrate the quantum theory for mesoscopic electric circuits and its applications. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a result, a new kind of commutation relation for electric charge and current occurred inevitably. The charge representation, canonical current representation and pseudo-current representation are discussed extensively. It not only provides a concrete realization of mathematical models which discuss the space quantization in high energy physics and quantum gravity but also presents a sequence of applications in condensed matter physics from a different point of view. A possible generalization to coupled circuits is also proposed.

cond-mat.mes-hall↗
arXiv2000

Theory of electrons with orbital degeneracy

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SU_d(4) symmetry of spin-orbital double. A hidden charge SU_c(4) symmetry is exposed and an extended Lieb-Mattis transformation which maps these two symmetries into each other is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6) Heisenberg magnet at half-filling and a SU(4) one at quarter-filling. The band is half-filled at all temperature for $μ=3U/2$. The features of ground state and low-lying excitations in one dimension are indicated according to exact solutions. Various possibilities of symmetry breaking are also given.

cond-mat.str-el↗
arXiv2000

One dimensional model for doubly degenerate electrons

A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite N number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving the Bethe-ansatz equation numerically. For infinite N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit.

cond-mat.str-el↗
arXiv1999

Some aspects of functional Bethe ansatz

The validity of Bethe ansatz wave function without the backward scattering for the problem of impurity in correlated hosts with periodic boundary condition is illustrated by a simple example of quantum mechanics. An long being overlooked point in solving Hubbard model by means of Bethe ansatz is indicated. A possible repairing on the Hamiltonian is suggested so that the well known solution is still valid.

cond-mat↗
arXiv1999

Ground State and Excitations of Spin Chain with Orbital Degeneracy

The one dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric viewpoint by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

cond-mat.str-el↗
arXiv1999

Quantum Theory for Mesoscopic Electric Circuits and Its Applications

This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is addressed. The mesoscopic LC-design is quantized in accord with the charge discreteness. The uncertainty relation for electric charge and current is given. Because the stationary Schrödinger equation is turned to be Mathieu equation in $p$-representation, the wave function and energy spectrum is formally solved. As further applications, the persistent current is obtained by considering the mesoscopic ring as a pure L-design. The Coulomb blockade phenomenon occurs when applying the theory to the pure C-design. Concerning the time evolution of the states for mesoscopic electric circuit, we are able to study it by the method of characteristics. In order to study the dissipative effect in the circuit, we use density-matrix formulation. In this formulation, several type of ``off diagonal'' dissipations are expected to be discussed.

cond-mat.mes-hall↗
arXiv1999

Thermodynamics of Kondo Model with Electronic Interactions

On the basis of Bethe ansatz solution of one dimensional Kondo model with electronic interaction, the thermodynamics equilibrium of the system in finite temperature is studied in terms of the strategy of Yang and Yang. The string hypothesis in the spin rapidity is discussed extensively. The thermodynamics quantities, such as specific heat and magnetic susceptibility, are obtained.

cond-mat.str-el↗
arXiv1997

The Hubbard quantum wire

By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly obtained. The ground state and low-lying excited states are studied in the thermodynamic limit. The ground-state energy in the strong coupling limit is obtained explicitly, and compared with the results of periodic boundary condition.

cond-mat.str-el↗
arXiv1997

Exact results for a Kondo impurity with electronic correlations

An one dimensional model of a Kondo impurity with arbitrary spin in the presence of electronic correlations is solved exactly. The Bethe ansatz equations are obtained for the case of quadratic dispersion. The ground state is studied in the thermodynamic limit, and the magnetic susceptibility at zero temperature is calculated.

cond-mat.str-el↗
arXiv1997

Mesoscopic quantum circuit theory to the persistent current and Coulomb blockade

The quantum theory for mesoscopic electric circuit is briefly described. The uncertainty relation for electric charge and current modifies the tranditional Heisenberg uncertainty relation. The mesoscopic ring is regarded as a pure L-design, and the persistent current is obtained explicitly. The Coulomb blockade phenomenon appears when applying to the pure C-design.

cond-mat.mes-hall↗
arXiv1996

Exact results of a hard-core interacting system with a single impurity

The quantum-mechanical problem of a many-particle system with a single impurity in one-dimension, interacting by a delta-function, is solved. The wave-function for a bosonic system and the related secular equation for the spectrum are obtained. The energy per length is calculated in the thermodynamic limit.

cond-mat↗
arXiv1996

Prolongation Approach to Bäcklund Transformation of Zhiber-Mikhailov-Shabat Equation

The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-B$\ddot{a}$cklund transformation of ZMS equation is obtained.

hep-th↗
arXiv1996

An exactly solvable model of the persistent currents in presence of hard-core interaction in a one dimensional mesoscopic ring

A simplest model of the persistent current in presence of many-body interaction in a mesoscopic ring is presented. The Bethe ansatz approach is used to find exact solutions. Both cases in the absence of impurity and in the presence of impurity are solved and compared. It is indicated that both impurity and hard-core interaction do not affect the result of persistent current explicitly if there is a large number of electrons in the ring.

cond-mat↗
arXiv1996

$δ$-function spin-1/2 fermions in a one-dimensional potential well

The quantum-mechanical problem of $N$ fermions with $δ$-function interaction in a one-dimensional potential well of finite depth is solved. It is shown that there exists exact wave function of Bethe-ansatz form in the case that a single particle tunnels outside of the well. The Bethe-ansatz like secular equations for the spectrum are obtained.

hep-th↗
arXiv1996

Quantum theory for mesoscopic electric circuits

A quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges is proposed. On the basis of the theory, Schrödinger equation for the quantum LC-design and L-design is solved exactly. The uncertainty relation for electric charge and current is obtained and a minimum uncertainty state is solved. By introducing a gauge field, a formula for persistent current arising from magnetic flux is obtained from a new point of view.

cond-mat↗