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On quantum microcanonical equilibrium
Dorje C. Brody, Daniel W. Hook, Lane P. Hughston
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived,…
Entanglement of three-qubit geometry
Dorje C. Brody, Anna C. T. Gustavsson, Lane P. Hughston
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometr…
PT-Symmetric Extension of the Korteweg-de Vries Equation
Carl M. Bender, Dorje C. Brody, Junhua Chen +1
The Korteweg-de Vries equation u_t+uu_x+u_{xxx}=0 is PT symmetric (invariant under space-time reflection). Therefore, it can be generalized and extended into the complex domain in…
Faster than Hermitian Quantum Mechanics
Carl M. Bender, Dorje C. Brody, Hugh F. Jones +1
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the follo…
Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
Carl M. Bender, Dorje C. Brody, Jun-Hua Chen +3
In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian $\cP\cT$-symmetric wrong-sign quartic Hamiltonian $H=\half p^2-gx^4$ has the same spectrum…
Combinatorics and field theory
Carl M. Bender, Dorje C. Brody, Bernhard K. Meister
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method emp…
On optimum Hamiltonians for state transformations
Dorje C. Brody, Daniel W. Hook
For a prescribed pair of quantum states |psi_I> and |psi_F> we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates t…
Quantum states and space-time causality
Dorje C. Brody, Lane P. Hughston
Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoher…