Lyapunov equation in open quantum systems and non-Hermitian physics

Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT -symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψi〉 into a specific final state |ψf 〉 can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two...

Coherent states of non-Hermitian quantum systems

We use the Gazeau-Klauder formalsim to construct coherent states of non-Hermitian quantum systems. In particular we use this formalism to construct coherent state of a PT symmetric system. We also describe the construction of coherent states following Klauder’s minimal prescription. e-mail : [email protected] e-mail : [email protected]

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems

Non-hermitian quantum thermodynamics.

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal...

Hermitian metric on quantum spheres

The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.