Exactly Solvable Model of Quantum Diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band. The subsystem interacts with its environment by a coupling expressed in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wave number contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. An analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling     

Remarks on Exactly Solvable Noncommutative Quantum Field

We study exactly the solvable noncommutative scalar quantum field models of （2n） or （2n ＋ 1） dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B. 0 = 4-1 in field theoretic context means the full restoration of the maximal U（∞） gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1＋1-dimensional Moyal/matrix-valued nonlinear Schr6dinger （MNLS） equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.     

Higher Order Generation of Exactly Solvable Supersymmetric Systems

Starting from an exactly solvable potential, itis shown that it is always possible to construct aninfinite set of higher order generation supersymmetricsystems which are also exactly solvable. A method of deriving these potentials is presented andthe corresponding eigenfunctions and eigenspectra arediscussed. The theory is illustrated with an example inwhich the first- and second-order generation systems are considered.     

Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials

In this paper, we establish the underlying quantum dynamical algebra SU(1,1) for some one-dimensional exactly solvable potentials by using the shift operators method. The connection between SU(1,1) algebra and the radial Hamiltionian problems is also discussed. PACS numbers: 03.65.Ge     

Exactly Solvable Model of a Two-Level Quantum System Interacting with Spin Environment

An exactly solvable model of a two-level quantum system interacting with spin environment is considered. The interaction is assumed to be such that the state of the environment is conserved. Dynamics of the reduced density matrix of the two-level system is calculated for arbitrary coupling strength. The stationary state of the spin is obtained explicitly in the t limit.     

Gamow Vectors in Exactly Solvable Models

Through two examples: the Friedrichs model and a particular case of central potential scattering, we illustrate the way of constructing Gamow vectors.     

Raising and Lowering Operators for a Class of Exactly Solvable Quantum Nonlinear Harmonic Oscillators

In this paper, we study a new class of exactly solvable quantum nonlinear harmonic oscillators from the viewpoint of the raising and lowering operators. The energy spectrum for the Hamiltonian and the ground state are also given explicitly.     

Exactly Solvable Models and Spontaneous Symmetry Breaking

We study a few two-dimensional models with massless and massive fermions in the hamiltonian framework and in both conventional and light-front (LF) forms of field theory. The new ingredient is a modification of the canonical procedure by taking into account solutions of the operator field equations. After summarizing the main results for the derivative-coupling and the Thirring models, we briefly compare conventional and LF versions of the Federbush model including the massive current bosonization and a Bogoliubov transformation to diagonalize the Hamiltonian. Then we sketch an extension of our hamiltonian approach to the two-dimensional Nambu–Jona-Lasinio model and the Thirring-Wess model. Finally, we discuss the Schwinger model in a covariant gauge. In particular, we point out that the solution due to Lowenstein and Swieca implies the physical vacuum in terms of a coherent state of massive scalar field and suggest a new formulation of the model’s vacuum degeneracy.     

Quantum Tunneling in Time-Dependent Potential Barrier: a General Formulation and Some Exactly Solvable Models

Quantum tunneling in one spatial dimension in the presence of time-dependent potentials is investigated theoretically. First, a general multichannel formulation of the problem is given for harmonic time-dependence. The case of an oscillatory delta-function potential of constant strength is discussed at length and specific numerical calculations are presented for the reflection and transmission coefficients. Then other exactly solvable time-dependent potentials are obtained by carrying out successive unitary transformations. As an example of this class, a delta-function potential with time-dependent strength and boundary conditions is studied. Finally tunneling time-delay for time-dependent potentials is formulated in the multichannel situation, and also the concept of first passage time for the decay of a wave packet confined to one well of a double well potential is generalized for the case of time-dependent barrier and boundary conditions.     

Perfect Transfer of Many-Particle Quantum State via High-Dimensional Systems with Spectrum-Matched Symmetry

The quantum state transmission through the medium of high-dimensional many-particle system (boson or spinless fermion) is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor (NN). We also study a simple but realistic near half-filled tight-binding fermion system with uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.     

Is the Two-Dimensional One-Component Plasma Exactly Solvable?

The model under consideration is the two-dimensional (2D) one-component plasma of point-like charged particles in a uniform neutralizing background, interacting through the logarithmic Coulomb interaction. Classical equilibrium statistical mechanics is studied by non-traditional means. The question of the potential integrability (exact solvability) of the plasma is investigated, first at arbitrary coupling constant Γ via an equivalent 2D Euclidean-field theory, and then at the specific values of Γ = 2*integer via an equivalent 1D fermionic model. The answer to the question in the title is that there is strong evidence for the model being not exactly solvable at arbitrary Γ but becoming exactly solvable at Γ = 2*integer. As a by-product of the developed formalism, the gauge invariance of the plasma is proven at the free-fermion point Γ = 2; the related mathematical peculiarity is the exact inversion of a class of infinite-dimensional matrices.     

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

Rieffel's Deformation Quantization and Isospectral Deformations

We demonstrate the relation between the isospectral deformation and Rieffel's deformation quantization by the action of ⁿ .     

Generation of Exactly Solvable Non-Hermitian Potentials with Real Energies

Series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.