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Quantum phase transitions without thermodynamic limits
Dorje C. Brody, Daniel W. Hook, Lane P. Hughston
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level sur…
Exactly solvable quantum state reduction models with time-dependent coupling
Dorje C. Brody, Irene C. Constantinou, James D. C. Dear +1
A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed dire…
Semiclassical analysis of a complex quartic Hamiltonian
Carl M. Bender, Dorje C. Brody, Hugh F. Jones
It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\halfμ^2x^2-λx^4 in order to demonstrate that H defines a consistent unitary…
Quantum noise and stochastic reduction
Dorje C. Brody, Lane P. Hughston
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a q…
Solvable model of quantum microcanonical states
Carl M Bender, Dorje C Brody, Daniel W Hook
This letter examines the consequences of a recently proposed modification of the postulate of equal {\it a priori} probability in quantum statistical mechanics. This modification,…
Microcanonical distributions for quantum systems
Dorje C Brody, Daniel W Hook, Lane P Hughston
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpos…
Finite-time stochastic reduction models
Dorje C. Brody, Lane P. Hughston
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-…