Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExact dynamics of XX central spin models
136
0
0.0
(
0
)
Added by
Anastasia Jivulescu
Publication date
2009
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrodinger equation of the spin system model is solved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed.
rate research
Read More
We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} simeqfrac{pi N}{A} m$ for a large $N$. For $Delta =0$, $Nto infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity.
We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free energy, in the thermodynamic limit, follows from its semiclassical limit. Analysis of singularities of the equations of state reveals the occurrence of phase transitions of nematic type at not zero external fields and allows for an interpretation of the phase transitions in terms of shock dynamics in the space of thermodynamics variables. The approach is shown at work in the case of a q-state model for q=3 but the method generalises to arbitrary q.
An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The ground state and the elementary excitations are also studied. It is shown that the spinon excitation of the present model possesses a novel triple arched structure. The elementary excitation is gapless if the anisotropic parameter $eta$ is real while the elementary excitation has an enhanced gap by the next-nearest-neighbour and chiral three-spin interactions if the anisotropic parameter $eta$ is imaginary. The method of this paper provides a general way to construct new integrable models with next-nearest-neighbour interactions.
For the high-dimensional Kuramoto model with identical oscillators under a general digraph that has a directed spanning tree, although exponential synchronization was proved under some initial state constraints, the exact exponential synchronization rate has not been revealed until now. In this paper, the exponential synchronization rate is precisely determined as the smallest non-zero real part of Laplacian eigenvalues of the digraph. Our obtained result extends the existing results from the special case of strongly connected balanced digraphs to the condition of general digraphs owning directed spanning trees, which is the weakest condition for synchronization from the aspect of network structure. Moreover, our adopted method is completely different from and much more elementary than the previous differential geometry method.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
