Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPrepotential approach to systems with dynamical symmetries
139
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have the symmetries which are similar to the corresponding ones, and can be solved by using the algebraic method.
rate research
Read More
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy can be represented in the oscillator-like form in terms of pseudofermionic creation and annihilation operators for both real and complex eigenvalues. The example of most general four-level traceless Hamiltonian with odd time-reversal symmetry, which is an extension of the SO(5) Hermitian Hamiltonian, is considered in greater and explicit detail.
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosakis formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an orbifolded -- in the sense of conditional expectation -- system in terms of the Jones index. We take the opportunity to point out entropic certainty relation for arbitrary von Neumann subalgebras of a factor related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.
Symmetries are fundamental to dynamical processes in complex networks such as cluster synchronization, which have attracted a great deal of current research. Finding symmetric nodes in large complex networks, however, has relied on automorphism groups in algebraic group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each and every node in the network. We prove mathematically that nodes with the identical SPV are symmetrical to each other. Utilizing six representative complex networks from the real world, we demonstrate that all symmetric nodes can be found in linear time, and the SPVs can not only characterize the similarity of nodes but also quantify the nodal influences in spreading dynamics on the network. Our SPV-based framework, in additional to being rigorously justified, provides a physically intuitive way to uncover, understand and exploit symmetric structures in complex networks.
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohms quantum trajectories can be based. An application to the two dimensional isotropic harmonic oscillator is presented as an illustration.
We show that the generalization of the relative entropy of a resource from states to channels is not unique, and there are at least six such generalizations. We then show that two of these generalizations are asymptotically continuous, satisfy a version of the asymptotic equipartition property, and their regularizations appear in the power exponent of channe
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
