The equivalence between Floquet formalism and the multi-step approach in computing the evolution operator of a periodical time-dependent Hamiltonian

1998 ◽  
Vol 288 (2-4) ◽  
pp. 230-234 ◽  
Author(s):  
Shangwu Ding ◽  
Charles A McDowell
Keyword(s):  
Evolution Operator ◽  
Time Dependent

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

THE QUADRATIC TIME-DEPENDENT HAMILTONIAN: EVOLUTION OPERATOR, SQUEEZING REGIONS IN PHASE SPACE AND TRAJECTORIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1563-1576 ◽  
Author(s):  
S.S. MIZRAHI ◽  
M.H.Y. MOUSSA ◽  
B. BASEIA
Keyword(s):  
Phase Space ◽  
Unitary Transformation ◽  
Uniform Magnetic Field ◽  
Evolution Operator ◽  
Single Mode ◽  
Time Dependent ◽  
Special Cases ◽  
Complete Set ◽  
Hamiltonian Evolution ◽  
General Time

We consider the most general Time-Dependent (TD) quadratic Hamiltonian written in terms of the bosonic operators a and a+, which may represent either a charged particle subjected to a harmonic motion, immersed in a TD uniform magnetic field, or a single mode photon field going through a squeezing medium. We solve the TD Schrödinger equation by a method that uses, sequentially, a TD unitary transformation and the diagonalization of a TD invariant, and we verify that the exact solution is a complete set of TD states. We also obtain the evolution operator which is essential to express operators in the Heisenberg picture. The variances of the quadratures are calculated and a phase space of parameters introduced, in which we identify squeezing regions. The results for some special cases are presented and as an illustrative example the parametric oscillator is revisited and the trajectories in phase space drawn.

scholarly journals Specifying the Unitary Evolution of a Qudit for a General Nonstationary Hamiltonian via the Generalized Gell-Mann Representation

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 521
Author(s):  
Elena R. Loubenets ◽  
Christian Käding
Keyword(s):  
Vector Space ◽  
Wide Class ◽  
Analytical Study ◽  
Evolution Operator ◽  
Unit Vector ◽  
Time Dependent ◽  
Unitary Evolution ◽  
Analytical Expression ◽  
Optimal Realizations ◽  
Quantum Technology

Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a d-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit ( d ≥ 2 ) in terms of the Bloch-like vector space and specify how, in a general case, this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case ( d = 2 ) , we specify the unitary evolution of a qubit via the evolution of a unit vector in R 4 , and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.

A CLOSED-FORM SOLUTION OF THE EVOLUTION OPERATOR IN TWO-LEVEL SYSTEMS

1994 ◽  
Vol 08 (08n09) ◽  
pp. 505-508 ◽  
Author(s):  
XIAN-GENG ZHAO
Keyword(s):  
Closed Form ◽  
Lie Algebra ◽  
Evolution Operator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Two Level Systems ◽  
Special Case

It is demonstrated by using the technique of Lie algebra SU(2) that the problem of two-level systems described by arbitrary time-dependent Hamiltonians can be solved exactly. A closed-form solution of the evolution operator is presented, from which the results for any special case can be deduced.

DYNAMICAL PROPERTIES OF MULTI-PHOTON INTERACTION BETWEEN A CAVITY FIELD AND A SINGLE-QUBIT

2013 ◽  
Vol 11 (04) ◽  
pp. 1350038 ◽  
Author(s):  
HEBA KADRY ◽  
NORDIN ZAKARIA ◽  
LEE YEN CHEONG ◽  
MAHMOUD ABDEL-ATY
Keyword(s):  
Evolution Operator ◽  
Cooper Pair ◽  
Time Dependent ◽  
Cooper Pairs ◽  
Cavity Field ◽  
Field Coupling ◽  
Single Qubit ◽  
Cooper Pair Box ◽  
The Mean ◽  
Dynamical Properties

We study the dynamical properties of a cavity field coupling to a Cooper pair box (CPB). We assumed that the CPB is prepared initially in a mixed state with a coherent state for the field. By solving the time-dependent equations using the evolution operator, it shows that mean numbers of Cooper pairs is affected by the detuning. The mean number of Cooper pairs is further enhanced by the multi-photon processes in commonly used cavity field.

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

1994 ◽  
Vol 08 (14n15) ◽  
pp. 917-927 ◽  
Author(s):  
A. JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Evolution Operator ◽  
Variable Mass ◽  
Time Dependent ◽  
Integral Approach ◽  
Feynman Path ◽  
Time Evolution Operator ◽  
General Time

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

scholarly journals EVOLUTION OPERATOR AND WAVE FUNCTION OF A TIME-DEPENDENT OSCILLATOR

1999 ◽  
Vol 48 (9) ◽  
pp. 1601
Author(s):  
XU XIU-WEI ◽  
LIU SHENG-DIAN ◽  
REN TING-QI ◽  
ZHANG YONG-DE
Keyword(s):  
Wave Function ◽  
Evolution Operator ◽  
Time Dependent
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