Tatsuo Suzuki

Nonlinear Grassmann sigma models in any dimension and an infinite number of conserved currents

Abstract We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therefore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, G / H sigma models in any dimension.

GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR

In this paper the general solution of the quantum damped harmonic oscillator is given.

Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P1-model, Q P1-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.

AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION II: ANOTHER APPROACH

In the preceding paper (arXiv:1103.0329 [math-ph]) we treated the Jaynes-Cummings model with dissipation and gave an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion. nHowever, to obtain a compact form of the approximate solution (which is in general complicated infinite series) is very hard when an initial condition is given. To overcome this difficulty we develop another approach and obtain a compact approximate solution when some initial condition is given.

An Approximate Solution of the Jaynes-Cummings Model with Dissipation

In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {bf under the general setting} by making use of the Zassenhaus expansion.

General solution of the quantum damped harmonic oscillator II: Some examples

In the preceding paper (arXiv : 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.

On the magic matrix by Makhlin and the B-C-H formula in SO(4)

A closed expression to the Baker–Campbell–Hausdorff (B-C-H) formula in SO(4) is given by making use of the magic matrix by Makhlin. As far as we know this is the first nontrivial example on (semi–) simple Lie groups summing up all terms in the B-C-H expansion.

Quantum Diagonalization Method in the Tavis-Cummings Model

To obtain the explicit form of evolution operator in the Tavis–Cummings model we must calculate the term e-itg(S+⊗a+S-⊗ a† explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S+ ⊗ a +S- ⊗ a† diagonal to calculate e-itgA and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is the first nontrivial examples as far as we know, and reproduce the calculations of e-itgA given in quant-ph/0404034. We also give a hint to an application to non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

SUBMODELS OF NONLINEAR GRASSMANN SIGMA MODELS IN ANY DIMENSION AND CONSERVED CURRENTS, EXACT SOLUTIONS

In the preceding paper,1 we constructed submodels of nonlinear Grassmann sigma models in any dimensions and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this letter, we first construct almost all conserved currents for the submodels and all those for CP1-model. We next review the Smirnov and Sobolev construction for the equations of CP1-submodel and extend the equations, the S-S construction and conserved currents to higher order ones.

MORE ON THE ISOMORPHISM SU(2) ⊗ SU(2) ≅ SO(4)

In this paper, we revisit the isomorphism SU(2) ⊗ SU(2) ≅ SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix Q by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n) which characterizes entanglements in the case of n = 2 is studied, and a clear-cut calculation of the universal Yang–Mills action in (hep-th/0602204) is given for the abelian case.