Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Husimi Rhombus Lattice with Random Angles to Present the Space Stochasticity in Exact Thermodynamic Calculation
68
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Dr. Chengjie Wu and Dr. Chong Chen provided computation resource and helped in the code programming, however they believe they did not contribute to the scientific part therefore consider not to be listed as authors. Thus authors agree to replace the manuscript with updated author list.
rate research
Read More
We develop a theoretical approach to ``spontaneous stochasticity in classical dynamical systems that are nearly singular and weakly perturbed by noise. This phenomenon is associated to a breakdown in uniqueness of solutions for fixed initial data and underlies many fundamental effects of turbulence (unpredictability, anomalous dissipation, enhanced mixing). Based upon analogy with statistical-mechanical critical points at zero temperature, we elaborate a renormalization group (RG) theory that determines the universal statistics obtained for sufficiently long times after the precise initial data are ``forgotten. We apply our RG method to solve exactly the ``minimal model of spontaneous stochasticity given by a 1D singular ODE. Generalizing prior results for the infinite-Reynolds limit of our model, we obtain the RG fixed points that characterize the spontaneous statistics in the near-singular, weak-noise limit, determine the exact domain of attraction of each fixed point, and derive the universal approach to the fixed points as a singular large-deviations scaling, distinct from that obtained by the standard saddle-point approximation to stochastic path-integrals in the zero-noise limit. We present also numerical simulation results that verify our analytical predictions, propose possible experimental realizations of the ``minimal model, and discuss more generally current empirical evidence for ubiquitous spontaneous stochasticity in Nature. Our RG method can be applied to more complex, realistic systems and some future applications are briefly outlined.
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.
A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence. It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase. A thermally-assisted reentrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.
A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the sense that the entropy density is zero in the thermodynamic limit. The existence of a thermodynamic transition associated with such irregularly ordered ground states is conjectured from a duality relation for a thermodynamic function. This conjecture is supported by a phenomenological argument and numerical experiments.
When masless excitations are limited or modified by the presence of material bodies one observes a force atcing between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) surface of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below the finite-size critical point.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
