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Register a new userEffective Hamiltonian, Mori Product and Quantum Dynamics
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An appropriate extension of the effective potential theory is presented that permits the approximate calculation of the dynamical correlation functions for quantum systems. These are obtained by evaluating the generating functionals of the Mori products of quantities related to the relaxation functions in the (PQSCHA) pure self consistent harmonic approximation.
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The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the olomorphic path integral for the Weyl symbol of the density matrix, makes it possible to directly approach general Hamiltonians given in terms of bosonic creation and annihilation operators.
The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian - depending on quantum coupling and temperature - and classical-like expressions for the averages of observables. In this work the PQSCHA is derived in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the path integral for the Weyl symbol of the density matrix, makes it possible to approach directly general Hamiltonians given in terms of bosonic creation and annihilation operators.
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, such as ring polymer and centroid molecular dynamics, which allow the approximate calculation of both quantum statistical and quantum dynamical properties. To this end, we derive a new integration algorithm which also makes use of multiple time-stepping. The scheme is validated via adaptive classical--path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as possible. By applying a local rewiring move, the network reaches equilibrium states assuming broad degree distributions, which have a power law form in an intermediate range of the parameters used. Interestingly, in the same range we find non-trivial hierarchical clustering.
We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the kinetic energy and a decrease in the potential energy, with the total energy being conserved. We find that the coarsening dynamics exhibits a consistently superdiffusive growth of a characteristic length scale with 1/z > 1/2 (ranging from 0.54 to 0.57). Also, the number of point defects (vortices and antivortices) decreases with exponents ranging between 1.0 and 1.1. On the other hand, the excess potential energy decays with a typical exponent of 0.88, which shows deviations from the energy-scaling relation. The spin autocorrelation function exhibits a peculiar time dependence with non-power law behavior that can be fitted well by an exponential of logarithmic power in time. We argue that the conservation of the total Josephson (angular) momentum plays a crucial role for these novel features of coarsening in the Hamiltonian XY model.
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