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Quasiclassical approximation for models of spin-spin interaction on a one-dimensional lattice

Yu. M. Vorob'ev, S. Yu. Dobrokhotov, Виктор Павлович Маслов

Journal of Mathematical SciencesDec 1, 19850 citations

Quasiclassical Perturbation Theory for Time-Dependent Expectation Values with Quantum Nonlinear Hamiltonians

Lecture notes in physics. M, MonographsJan 1, 19940 citations

Quasiclassical approximation for the spin-boson Hamiltonian with counterrotating terms

G. A. Finney, Julio R. Gea-Banacloche

We derive quasiclassical (approximately factorizable) trajectories for the spin-boson Hamiltonian without the rotating-wave approximation (RWA) and show how they may be used to calculate the evolution of the fully quantized system when the initial state of the oscillator (boson field) is a coherent state with sufficiently large amplitude. We give a general prescription to obtain such trajectories for other systems. We study how well-known features of the model in the RWA are modified by the counterrotating terms and explore some of the new phenomenology introduced by these terms.We derive quasiclassical (approximately factorizable) trajectories for the spin-boson Hamiltonian without the rotating-wave approximation (RWA) and show how they may be used to calculate the evolution of the fully quantized system when the initial state of the oscillator (boson field) is a coherent state with sufficiently large amplitude. We give a general prescription to obtain such trajectories for other systems. We study how well-known features of the model in the RWA are modified by the counterrotating terms and explore some of the new phenomenology introduced by these terms.

Physical Review ASep 1, 199425 citations

Quasiclassical Hamiltonians for large-spin systems.

Dmitry A. Garanin, K. Kladko, Peter Fulde

We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.

Jan 1, 20006 citations

Semi-Classical Dynamics in Quantum Spin Systems

Jürg Martin Fröhlich, Antti Knowles, Enno Lenzmann

arXiv:0709.4561Letters in Mathematical PhysicsNov 19, 200712 citations

On model spin Hamiltonians including long-range ferromagnetic interaction

J.G. Brankov, A.S. Shumovsky, Valentin Anatol'evich Zagrebnov

PhysicaNov 1, 197425 citations

Quasiclassical Hamiltonians for large-spin systems

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