Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSimulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories
93
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Going to higher orders of the BBGKY hierarchy allows for a systematic refinement of the method. Quantum correlations are treated through both, the Wigner function sampling and the BBGKY evolution, bringing about highly accurate estimates of correlation functions. The method is particularly suitable for long-range interacting systems, and we demonstrate its power by comparing with exact results as well as other numerical methods. As an application we compute spin squeezing in a two-dimensional lattice with power-law interactions and a transverse field, which should be accessible in future ion trap experiments.
rate research
Read More
Atomistic simulations of thermodynamic properties of magnetic materials rely on an accurate modelling of magnetic interactions and an efficient sampling of the high-dimensional spin space. Recent years have seen significant progress with a clear trend from model systems to material specific simulations that are usually based on electronic-structure methods. Here we develop a Hamiltonian Monte Carlo framework that makes use of auxiliary spin-dynamics and an auxiliary effective model, the temperature-dependent spin-cluster expansion, in order to efficiently sample the spin space. Our method does not require a specific form of the model and is suitable for simulations based on electronic-structure methods. We demonstrate fast warm-up and a reasonably small dynamical critical exponent of our sampler for the classical Heisenberg model. We further present an application of our method to the magnetic phase transition in bcc iron using magnetic bond-order potentials.
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.
We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, a dissipative version of the quantum Ising model, and the micromaser. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and in general dynamical phase behavior needs to be uncovered by observables which are strictly dynamical, e.g. dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.
We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose-Einstein employing the Keldysh-Schwinger approach and develop the renormalization group technique that enables us to obtain analytical expressions for temperature dependencies of critical exponents.
We introduce a Maxwell demon which generates many-body-entanglement robustly against thermal fluctuations, which allows us to obtain quantum advantage. Adopting the protocol of the voter model used for opinion dynamics approaching consensus, the demon randomly selects a qubit pair and performs a quantum feedback control, in continuous repetitions. We derive a lower bound of the entropy production rate by demons operation, which is determined by a competition between the quantum-classical mutual information acquired by the demon and the absolute irreversibility of the feedback control. Our finding of the lower bound corresponds to a reformulation of the second law of thermodynamics under a stochastic and continuous quantum feedback control.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
