Spin Coherent State Representation Research Articles

Quantum simulation of ferromagnetic and anti-ferromagnetic tunneling anisotropic magnetoresistance in a single-molecule-magnet dimer tunnel-junction

In this work, we simulate the tunneling anisotropic magnetoresistance (TAMR) in a single-molecule-magnet (SMM) dimer tunnel-junction with metal and ferromagnetic (FM) electrodes. The non-collinear polarization of electrode with respect to the uniaxial anisotropy-axis of magnet results in both the FM and anti-ferromagnetic (AFM) TAMR respectively for the FM and AFM inter-molecule couplings. In terms of the spin coherent state representation of electron spin the non-collinear tunneling is able to be analyzed with the usual rate equation approach in a sequential tunneling regime. The ferromagnetic TAMR varies with the non-collinear angle and the tunneling magnetoresistance (TMR) is just a special case of the angle θ = π. With the FM dimer we obtain the higher TMR up to 400% and the high polarization rate (79%) of spin current as well. The angle dependence of TAMR for the AFM dimer is also presented along with the spin current.

Quantum approach of mesoscopic magnet dynamics with spin transfer torque

We present a theory of magnetization dynamics driven by spin-polarized current in terms of the quantum master equation. In the spin coherent state representation, the master equation becomes a Fokker-Planck equation, which naturally includes the spin transfer and quantum fluctuation. The current electron scattering state is correlated to the magnet quantum states, giving rise to quantum correction to the electron transport properties in the usual semiclassical theory. In the large-spin limit, the magnetization dynamics is shown to obey the Hamilton-Jacobi equation or the Hamiltonian canonical equations.

Dynamics of quasi-species models with a complex spin coherent state representation

We investigate the dynamics of the parallel mutation-selection quasi-species model of biological evolution for various fitness landscapes. By using the semiclassical propagator for spin coherent states, for the linear fitness landscape, we find the expression for the transition rate from an arbitrary initial state to an arbitrary final state and expressions for the mean fitness and the surplus. For the sharp-peak fitness landscape, we find the solutions to the dynamics equation in two time regions and the crossover time which separates these two regions. Finally, we present a semiclassical method to derive analytic expressions for the dynamics of the mean fitness and the surplus for general symmetric fitness landscapes, and in case of the quadratic fitness landscape, we obtain the dynamics of the mean fitness consistent with previous results.

Spin Coherent State Representation of the Crow-Kimura and Eigen Models of Quasispecies Theory

We present a spin coherent state representation of the Crow-Kimura and Eigen models of biological evolution. We deal with quasispecies models where the fitness is a function of Hamming distances from one or more reference sequences. In the limit of large sequence length N, we find exact expressions for the mean fitness and magnetization of the asymptotic quasispecies distribution in symmetric fitness landscapes. The results are obtained by constructing a path integral for the propagator on the coset SU(2)/U(1) and taking the classical limit. The classical limit gives a Hamiltonian function on a circle for one reference sequence, and on the product of 2m−1 circles for m reference sequences. We apply our representation to study the Schuster-Swetina phenomena, where a wide lower peak is selected over a narrow higher peak. The quadratic landscape with two reference sequences is also analyzed specifically and we present the phase diagram on the mutation-fitness parameter phase space. Furthermore, we use our method to investigate more biologically relevant system, a model of escape from adaptive conflict through gene duplication, and find three different phases for the asymptotic population distribution.

QUANTUM-CLASSICAL CROSSOVER OF THE ESCAPE RATE IN THE NANO-FERROMAGNET WITH COMPLEX CRYSTAL SYMMETRY

We investigate the quantum-classical crossover of the escape rate in the nanoscale ferromagnetic particle with complex crystal symmetries placed in an external field along the hard anisotropy axis. We use the periodic instanton technique based on the spin coherent state representation and the condition of the first-order crossover to determine the type of crossover. In the high field limit of ∊(=1-Hc/H)→0 the crossover is found to be second-order. We also calculate the crossover temperature with leading order behavior of T0~∊1/2.

Oscillation of the tunnel splitting in nanospin systems within the particle-mapping formalism

The oscillation of tunnel splitting in the biaxial spin system within magnetic field along the anisotropy axis is analyzed within the particle mapping approach, rather than in the (\theta-\phi) spin coherent-state representation. In our mapping procedure, the spin system is transformed into a particle moving in the restricted $S^1$ geometry whose wave function subjects to the boundary condition involving additional phase shift. We obtain the new topological phase that plays the same role as the Wess-Zumino action in spin coherent-state representation. Considering the interference of two possible trajectories, instanton and anti-instanton, we get the identical condition for the field at which tunneling is quenched, with the previous result within spin coherent-state representation.

Quantum dynamics of a generalized Coleman-Hepp model

Studies on a generalized Coleman-Hepp model are done on the basis of a spin coherent state representation and a transformation property of the model Hamiltonian. Namely, transforming the original model Hamiltonian into a simpler form, we can determine time evolution of the whole system by successive applications of rotation operators in a spinor space. Dynamics of detector spins as well as that of an incident particle are fully discussed. Explicit numerical evaluations are also performed. Relevance of our solution to a generalized Cini model is also briefly mentioned.

Dynamical processes in a generalized Coleman–Hepp model

Dynamical processes in quantum system are studied on the basis of Coleman–Hepp model. We present a theoretical framework using a spin coherent state representation. This enables us to obtain averages and quasi-probability densities which give detailed information on the dynamics of a detector as well as an incident particle. Numerical calculations are also done.

Non-linearities in bipolaronic superconductivity

A pseudospin formulation of the bipolaron model in the spin coherent state representation is used to study the evolution of the order parameter. It is found that it leads to several interesting non linear characteristics reminiscent of superfluidity.

Periodically pulsed spin dynamics: Scaling behavior of semiclassical wave functions.

Quantum analogs of Kolmogorov-Arnol'd-Moser tori and chaos in a periodically pulsed single-spin system are studied in the semiclassical regime. Wave functions (quasienergy states) are described in a spin-coherent state representation. Their projected binary-phase patterns are characterized in terms of the fractal dimensions of their perimeters.

The Heisenberg ferromagnet in spin coherent state representation

A new approach to Heisenberg ferromagnet using the spin coherent state representation is developed. The differential operator representation of spin angular momentum operators is used to derive thec-number analogs of the basic quantum mechanical equations, viz., the Schrodinger, Bloch and Liouville equations for the Heisenberg ferromagnet. As an important illustration of our formulation, which has noad hoc assumptions and does not use any boson representation, the excitation spectrum for one, two and three spin waves is obtained. In these cases it is also shown that eigenvalue spectrum can be obtained by completely ignoring the kinematical interactions.

Generalized phase space method in spin systems-spin coherent state representation

A generalized phase space method for spin operators is developed. With the use of a spin coherent state representation, mapping rules from spin operators onto ac-number space are established; simple formulas to calculate the mappedc-number functions are also derived. A product theorem, which gives a way of mapping a product of operators, is obtained in an intuitive form. This can be advantageously used to transform a Liouville equation into ac-number equation. As an illustrative example, the method is applied to the Heisenberg model of a magnet.

Spin Coherent State Representation in Non-Equilibrium Statistical Mechanics

A new method of treating problems of spin systems is developed, in which spin operators are transformed into two kinds of boson operators according to Schwinger's method. Usual treatment of coherent state representation is generalized to spin systems with a fixed magnitude S . Some basic properties and the relations to the atomic coherent state are investigated rather in details. The method is applied to spin relaxation process and a corresponding Fokker-Planck type equation is obtained and solved to give a multiple relaxation process due to nonlinearities. It is shown that our formulation has several advantages over other ones in some respects.