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Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets

Annals of Physics, ISSN 0003-4916, 05/2018, Volume 392, pp. 323 - 339

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven...

Gaudin magnets | Knizhnik–Zamolodchikov equations | Integrable time-dependent Hamiltonians | Landau–Zener models | Landau-Zener models | PHYSICS, MULTIDISCIPLINARY | EQUATION | Knizhnik-Zamolodchikov equations | Magnetic fields | Analysis | Models

Gaudin magnets | Knizhnik–Zamolodchikov equations | Integrable time-dependent Hamiltonians | Landau–Zener models | Landau-Zener models | PHYSICS, MULTIDISCIPLINARY | EQUATION | Knizhnik-Zamolodchikov equations | Magnetic fields | Analysis | Models

Journal Article

Physics letters. A, ISSN 0375-9601, 2019, Volume 383, Issue 2-3, pp. 158 - 163

For a large class of time-dependent non-Hermitian Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT...

Time-dependent Schrödinger equation | Quasi-exactly solvable models | Non-Hermitian quantum mechanics | PT-symmetry | Lewis–Riesenfeld invariants | Lewis-Riesenfeld invariants | PHYSICS, MULTIDISCIPLINARY | REPRESENTATION | Time-dependent Schrodinger equation | Analysis | Quantum theory | Algebra | Physics - Quantum Physics

Time-dependent Schrödinger equation | Quasi-exactly solvable models | Non-Hermitian quantum mechanics | PT-symmetry | Lewis–Riesenfeld invariants | Lewis-Riesenfeld invariants | PHYSICS, MULTIDISCIPLINARY | REPRESENTATION | Time-dependent Schrodinger equation | Analysis | Quantum theory | Algebra | Physics - Quantum Physics

Journal Article

Physics Letters B, ISSN 0370-2693, 09/2016, Volume 760, Issue C, pp. 1 - 5

In this article, we have investigated collective effects of atomic nuclei in presence of a time-dependent potential in Davydov–Chaban Hamiltonian...

Davydov–Chaban Hamiltonian | Time-dependent potential | Lewis–Riesenfeld dynamical invariant method | HARMONIC-OSCILLATOR | INTERACTING-BOSON MODEL | FIELD | PHYSICS, NUCLEAR | COHERENT STATES | CLASSICAL LIMIT | ISOTOPES | Lewis-Riesenfeld dynamical invariant method | COLLECTIVE NUCLEAR-STATES | ASTRONOMY & ASTROPHYSICS | Davydov-Chaban Hamiltonian | PHYSICS, PARTICLES & FIELDS | Nuclear and High Energy Physics | Physics

Davydov–Chaban Hamiltonian | Time-dependent potential | Lewis–Riesenfeld dynamical invariant method | HARMONIC-OSCILLATOR | INTERACTING-BOSON MODEL | FIELD | PHYSICS, NUCLEAR | COHERENT STATES | CLASSICAL LIMIT | ISOTOPES | Lewis-Riesenfeld dynamical invariant method | COLLECTIVE NUCLEAR-STATES | ASTRONOMY & ASTROPHYSICS | Davydov-Chaban Hamiltonian | PHYSICS, PARTICLES & FIELDS | Nuclear and High Energy Physics | Physics

Journal Article

European journal of physics, ISSN 1361-6404, 2019, Volume 40, Issue 3, p. 035007

A conceptually simple physical interpretation of a conserved Hamiltonian. for a mechanical system with a time-dependent constraint is given...

thermodynamic potential | PHYSICS, MULTIDISCIPLINARY | time-dependent constraints | reservoir | EDUCATION, SCIENTIFIC DISCIPLINES | Lagrange formalism | Legendre transformation

thermodynamic potential | PHYSICS, MULTIDISCIPLINARY | time-dependent constraints | reservoir | EDUCATION, SCIENTIFIC DISCIPLINES | Lagrange formalism | Legendre transformation

Journal Article

Annals of Physics, ISSN 0003-4916, 06/2017, Volume 381, pp. 90 - 106

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations...

Separation of variables | Wei–Norman method | Explicit unitary transformations | Lie group contractions | Time dependent quadratic quantum Hamiltonians | CHARGED-PARTICLE | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | INVARIANTS | Wei-Norman method | MODEL | MOTION | LIMITABLE DYNAMICAL GROUPS | QUANTUM-MECHANICS | DIAGONALIZATION | EVOLUTION EQUATIONS | SP GROUPS | CANONICAL TRANSFORMATIONS | FOUR-DIMENSIONAL CALCULATIONS | PARTICLE PRODUCTION | MATHEMATICAL EVOLUTION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | HAMILTON-JACOBI EQUATIONS | HAMILTONIANS | TIME DEPENDENCE | QUANTUM FIELD THEORY

Separation of variables | Wei–Norman method | Explicit unitary transformations | Lie group contractions | Time dependent quadratic quantum Hamiltonians | CHARGED-PARTICLE | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | INVARIANTS | Wei-Norman method | MODEL | MOTION | LIMITABLE DYNAMICAL GROUPS | QUANTUM-MECHANICS | DIAGONALIZATION | EVOLUTION EQUATIONS | SP GROUPS | CANONICAL TRANSFORMATIONS | FOUR-DIMENSIONAL CALCULATIONS | PARTICLE PRODUCTION | MATHEMATICAL EVOLUTION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | HAMILTON-JACOBI EQUATIONS | HAMILTONIANS | TIME DEPENDENCE | QUANTUM FIELD THEORY

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2014, Volume 47, Issue 44, pp. 445302 - 10

A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented...

Quantum two-level system | Time-dependent Hamiltonian | Solvable model | time-dependent Hamiltonian | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | solvable model | quantum two-level system | Functions (mathematics) | Operators | Dynamic tests | Dynamics | Mathematical analysis | Evolution | Dynamical systems | Furnishings

Quantum two-level system | Time-dependent Hamiltonian | Solvable model | time-dependent Hamiltonian | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | solvable model | quantum two-level system | Functions (mathematics) | Operators | Dynamic tests | Dynamics | Mathematical analysis | Evolution | Dynamical systems | Furnishings

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2019, Volume 475, Issue 2226, p. 20190148

A new class of time-energy uncertainty relations is directly derived from the Schrodinger equations for time-dependent Hamiltonians...

SPEED | EVOLUTION | time-dependent Hamiltonians | MULTIDISCIPLINARY SCIENCES | time-energy uncertainty relations | adiabatic quantum computation | quantum computation | GEOMETRY | Physics - Quantum Physics

SPEED | EVOLUTION | time-dependent Hamiltonians | MULTIDISCIPLINARY SCIENCES | time-energy uncertainty relations | adiabatic quantum computation | quantum computation | GEOMETRY | Physics - Quantum Physics

Journal Article

International Journal of Modern Physics E, ISSN 0218-3013, 04/2016, Volume 25, Issue 4, p. 1650029

In this paper, Bohr Hamiltonian has been studied with the time-dependent potential...

exact time-dependent wave function | time-dependent potential | Bohr Hamiltonian | Lewis-Riesenfeld dynamical invariant | QUANTUM PHASE-TRANSITIONS | NUCLEAR | SYMMETRY | PARTICLE | PHYSICS, NUCLEAR | MODEL | PHYSICS, PARTICLES & FIELDS

exact time-dependent wave function | time-dependent potential | Bohr Hamiltonian | Lewis-Riesenfeld dynamical invariant | QUANTUM PHASE-TRANSITIONS | NUCLEAR | SYMMETRY | PARTICLE | PHYSICS, NUCLEAR | MODEL | PHYSICS, PARTICLES & FIELDS

Journal Article

Annals of physics, ISSN 0003-4916, 2010, Volume 325, Issue 9, pp. 1884 - 1912

... Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis–Riesenfeld dynamical invariant is given...

The time-dependent Schrödinger equation | Lewis–Riesenfeld dynamical invariant | Propagator | Quantum integrals of motion | Ermakov's equation | Cauchy initial value problem | Ehrenfest's theorem | Quantum damped oscillators | Green function | Caldirola–Kanai Hamiltonians | Lewis-Riesenfeld dynamical invariant | Caldirola-Kanai Hamiltonians | Ehrenfest s theorem | NONLINEAR SCHRODINGER-EQUATIONS | CHARGED-PARTICLE | PHYSICS, MULTIDISCIPLINARY | COHERENT STATES | ADIABATIC INVARIANTS | BERRY PHASE | Ermakov s equation | WAVE-FUNCTIONS | EVOLUTION | The time dependent Schrodinger equation | DEPENDENT HARMONIC-OSCILLATOR | SYSTEMS | QUANTIZATION | Quadratic programming | Quantum physics | Motion control | Construction | Operators | Integrals | Uniqueness | Initial value problems | Schroedinger equation | Invariants | Oscillators | DIFFERENTIAL EQUATIONS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL OPERATORS | ELECTRONIC EQUIPMENT | EQUATIONS | QUANTUM MECHANICS | FUNCTIONS | INTEGRALS | GREEN FUNCTION | EQUIPMENT | MECHANICS | WAVE EQUATIONS | OSCILLATORS | PARTIAL DIFFERENTIAL EQUATIONS | QUANTUM OPERATORS | HAMILTONIANS | TIME DEPENDENCE | PROPAGATOR

The time-dependent Schrödinger equation | Lewis–Riesenfeld dynamical invariant | Propagator | Quantum integrals of motion | Ermakov's equation | Cauchy initial value problem | Ehrenfest's theorem | Quantum damped oscillators | Green function | Caldirola–Kanai Hamiltonians | Lewis-Riesenfeld dynamical invariant | Caldirola-Kanai Hamiltonians | Ehrenfest s theorem | NONLINEAR SCHRODINGER-EQUATIONS | CHARGED-PARTICLE | PHYSICS, MULTIDISCIPLINARY | COHERENT STATES | ADIABATIC INVARIANTS | BERRY PHASE | Ermakov s equation | WAVE-FUNCTIONS | EVOLUTION | The time dependent Schrodinger equation | DEPENDENT HARMONIC-OSCILLATOR | SYSTEMS | QUANTIZATION | Quadratic programming | Quantum physics | Motion control | Construction | Operators | Integrals | Uniqueness | Initial value problems | Schroedinger equation | Invariants | Oscillators | DIFFERENTIAL EQUATIONS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL OPERATORS | ELECTRONIC EQUIPMENT | EQUATIONS | QUANTUM MECHANICS | FUNCTIONS | INTEGRALS | GREEN FUNCTION | EQUIPMENT | MECHANICS | WAVE EQUATIONS | OSCILLATORS | PARTIAL DIFFERENTIAL EQUATIONS | QUANTUM OPERATORS | HAMILTONIANS | TIME DEPENDENCE | PROPAGATOR

Journal Article

Science China Mathematics, ISSN 1674-7283, 8/2018, Volume 61, Issue 8, pp. 1353 - 1384

In this paper, we study the following stochastic Hamiltonian system in ℝ2d (a second order stochastic differential equation): $$d{\dot X_t} = b({X_t},{\dot X_t...

kinetic Fokker-Planck operator | stochastic Hamiltonian system | 60H10 | weak differentiability | Krylov’s estimate | Zvonkin’s transformation | Mathematics | Applications of Mathematics | BROWNIAN-MOTION | EXISTENCE | MATHEMATICS, APPLIED | TIME-DEPENDENT DRIFT | Zvonkin's transformation | EQUATIONS | SOBOLEV DIFFUSION-COEFFICIENTS | MATHEMATICS | REGULARITY | WEAK UNIQUENESS | DEGENERATE | SDES | Krylov's estimate

kinetic Fokker-Planck operator | stochastic Hamiltonian system | 60H10 | weak differentiability | Krylov’s estimate | Zvonkin’s transformation | Mathematics | Applications of Mathematics | BROWNIAN-MOTION | EXISTENCE | MATHEMATICS, APPLIED | TIME-DEPENDENT DRIFT | Zvonkin's transformation | EQUATIONS | SOBOLEV DIFFUSION-COEFFICIENTS | MATHEMATICS | REGULARITY | WEAK UNIQUENESS | DEGENERATE | SDES | Krylov's estimate

Journal Article

中国物理B：英文版, ISSN 1674-1056, 2015, Volume 24, Issue 8, pp. 159 - 165

Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH...

solution;inverse | time-dependent | quadratic | method | Hamiltonians;analytical | analytical solution | inverse method | Quadratic time-dependent Hamiltonians | CHAOS | MECHANICS | ORTHOGONAL FUNCTIONS INVARIANT | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | DYNAMICS | SYSTEMS | QUANTUM STATES | quadratic time-dependent Hamiltonians | Inverse problems | Mathematical analysis | Evolution | Gaussian | Inverse | Wave functions | Hamiltonian functions | Inverse method

solution;inverse | time-dependent | quadratic | method | Hamiltonians;analytical | analytical solution | inverse method | Quadratic time-dependent Hamiltonians | CHAOS | MECHANICS | ORTHOGONAL FUNCTIONS INVARIANT | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | DYNAMICS | SYSTEMS | QUANTUM STATES | quadratic time-dependent Hamiltonians | Inverse problems | Mathematical analysis | Evolution | Gaussian | Inverse | Wave functions | Hamiltonian functions | Inverse method

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2016, Volume 6, Issue 4, pp. 955 - 976

Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time-dependent quantum Hamiltonians (H) over cap...

Strichartz estimate | Herman-Kluk formula | Non-linear time-dependent Schrödinger equations | MATHEMATICS | MATHEMATICS, APPLIED | CONSTRUCTION | SCHRODINGER EVOLUTION-EQUATIONS | FORMULAS | Non-linear time-dependent Schrodinger equations | FUNDAMENTAL SOLUTION

Strichartz estimate | Herman-Kluk formula | Non-linear time-dependent Schrödinger equations | MATHEMATICS | MATHEMATICS, APPLIED | CONSTRUCTION | SCHRODINGER EVOLUTION-EQUATIONS | FORMULAS | Non-linear time-dependent Schrodinger equations | FUNDAMENTAL SOLUTION

Journal Article

International Journal of Modern Physics E, ISSN 0218-3013, 09/2016, Volume 25, Issue 9, p. 1650073

This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator...

time-dependent double ring shaped potential potential Lewis-Riesenfeld dynamical invariant method | time-dependent Manning-Rosen potential | time-dependent potential | Bohr Hamiltonian | PHYSICS, NUCLEAR | COHERENT STATES | PHYSICS, PARTICLES & FIELDS

time-dependent double ring shaped potential potential Lewis-Riesenfeld dynamical invariant method | time-dependent Manning-Rosen potential | time-dependent potential | Bohr Hamiltonian | PHYSICS, NUCLEAR | COHERENT STATES | PHYSICS, PARTICLES & FIELDS

Journal Article

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Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2017, Volume 50, Issue 25, p. 255205

In this paper, we apply the geometric Hamilton-Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure...

cosymplectic geometry | Jacobi geometry | dissipative terms | geometric Hamilton-Jacobi | time dependent hamiltonian systems | contact geometry | CONSTRAINT ALGORITHM | REDUCTION | PHYSICS, MULTIDISCIPLINARY | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | JACOBI EQUATION

cosymplectic geometry | Jacobi geometry | dissipative terms | geometric Hamilton-Jacobi | time dependent hamiltonian systems | contact geometry | CONSTRAINT ALGORITHM | REDUCTION | PHYSICS, MULTIDISCIPLINARY | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | JACOBI EQUATION

Journal Article

Physics letters. B, ISSN 0370-2693, 2007, Volume 650, Issue 2-3, pp. 208 - 212

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum...

Unitary | Metric operator | Time-dependent Hamiltonian | [formula omitted]-symmetry | Inner product | Pseudo-Hermitian | Geometric phase | PT-symmetry | metric operator | unitary | PHYSICS, NUCLEAR | FORMULATION | geometric phase | time-dependent Hamiltonian | SPACE | pseudo-Hermitian | MECHANICS | EVOLUTION | ASTRONOMY & ASTROPHYSICS | inner product | SPECTRUM | PHYSICS, PARTICLES & FIELDS

Unitary | Metric operator | Time-dependent Hamiltonian | [formula omitted]-symmetry | Inner product | Pseudo-Hermitian | Geometric phase | PT-symmetry | metric operator | unitary | PHYSICS, NUCLEAR | FORMULATION | geometric phase | time-dependent Hamiltonian | SPACE | pseudo-Hermitian | MECHANICS | EVOLUTION | ASTRONOMY & ASTROPHYSICS | inner product | SPECTRUM | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of physics. B, Atomic, molecular, and optical physics, ISSN 1361-6455, 2019, Volume 52, Issue 1, p. 015602

.... By means of a particular plane-wave expansion we arrive at a time-dependent Schrodinger equation governed by a Floquet Hamiltonian, which consists of convolutions of momentum and Fourier components...

Floquet Hamiltonian | high frequency | Toeplitz | Kramers-Henneberger | short pulse | envelope Hamiltonian | SUPERINTENSE | FIELDS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | HYDROGEN-ATOM | ADIABATIC STABILIZATION | MULTIPHOTON PROCESSES | ATOMIC STABILIZATION | TRANSITIONS | OPTICS | SPECTRA | IONIZATION

Floquet Hamiltonian | high frequency | Toeplitz | Kramers-Henneberger | short pulse | envelope Hamiltonian | SUPERINTENSE | FIELDS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | HYDROGEN-ATOM | ADIABATIC STABILIZATION | MULTIPHOTON PROCESSES | ATOMIC STABILIZATION | TRANSITIONS | OPTICS | SPECTRA | IONIZATION

Journal Article

The Journal of chemical physics, ISSN 1089-7690, 2018, Volume 148, Issue 14, p. 144707

.... Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms...

TIME-DEPENDENT TRANSPORT | CHEMISTRY, PHYSICAL | DOMAIN | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

TIME-DEPENDENT TRANSPORT | CHEMISTRY, PHYSICAL | DOMAIN | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 2018, Volume 127, pp. 32 - 45

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2D...

Jacobi’s last multiplier | Time-dependent Hamiltonian dynamics | Conformal Hamiltonian systems | Cosymplectic manifolds | Nambu–Hamiltonian systems | Jacobi's last multiplier | JACOBI LAST MULTIPLIER | NAMBU MECHANICS | DIFFERENTIAL-EQUATIONS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | MATHEMATICS | DYNAMICAL-SYSTEMS | Nambu-Hamiltonian systems | POISSON MANIFOLDS | CHAOTIC ATTRACTOR

Jacobi’s last multiplier | Time-dependent Hamiltonian dynamics | Conformal Hamiltonian systems | Cosymplectic manifolds | Nambu–Hamiltonian systems | Jacobi's last multiplier | JACOBI LAST MULTIPLIER | NAMBU MECHANICS | DIFFERENTIAL-EQUATIONS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | MATHEMATICS | DYNAMICAL-SYSTEMS | Nambu-Hamiltonian systems | POISSON MANIFOLDS | CHAOTIC ATTRACTOR

Journal Article

Physica Scripta, ISSN 0031-8949, 05/2016, Volume 91, Issue 6, p. 63014

.... Assuming that the time evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian...

shape coexistence | collective coordinates | microscopic theory of large-amplitude collective motion | time-dependent self-consistent mean field | Bohr-Mottelson collective Hamiltonian | quadrupole shape dynamics | TDHFB method | HARTREE-FOCK THEORY | GENERATOR-COORDINATE METHOD | PHYSICS, MULTIDISCIPLINARY | EVEN-EVEN NUCLEI | LARGE-AMPLITUDE MOTION | ANHARMONIC GAMMA-VIBRATIONS | RAPIDLY ROTATING NUCLEI | BOSON-EXPANSION THEORY | TIME-ODD COMPONENTS | RANDOM-PHASE-APPROXIMATION | CONSISTENT MEAN-FIELD | Physics - Nuclear Theory

shape coexistence | collective coordinates | microscopic theory of large-amplitude collective motion | time-dependent self-consistent mean field | Bohr-Mottelson collective Hamiltonian | quadrupole shape dynamics | TDHFB method | HARTREE-FOCK THEORY | GENERATOR-COORDINATE METHOD | PHYSICS, MULTIDISCIPLINARY | EVEN-EVEN NUCLEI | LARGE-AMPLITUDE MOTION | ANHARMONIC GAMMA-VIBRATIONS | RAPIDLY ROTATING NUCLEI | BOSON-EXPANSION THEORY | TIME-ODD COMPONENTS | RANDOM-PHASE-APPROXIMATION | CONSISTENT MEAN-FIELD | Physics - Nuclear Theory

Journal Article