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Phase-space measurements and decoherence for angular momentum systems
Dorje C. Brody, Eva-Maria Graefe, Rishindra Melanathuru
The monitoring of the three independent components of the angular momentum (or spin) of a quantum system by its environment that does not isolate any preferred orientation is model…
Quantum clock and Newtonian time
Dorje C. Brody, Lane P. Hughston
An extension of standard quantum mechanics is proposed in which the Newtonian time appearing as a parameter in the unitary evolution operator is replaced with the time shown by a `…
Decoherence from universal tomographic measurements
Dorje C. Brody, Rishindra Melanathuru
The decoherence phenomenon arising from an environmental monitoring of the state of a quantum system, as opposed to monitoring of a preferred observable, is worked out in detail us…
Phase-space measurements, decoherence and classicality
Dorje C. Brody, Eva-Maria Graefe, Rishindra Melanathuru
The emergence of classical behaviour in quantum theory is often ascribed to the interaction of a quantum system with its environment, which can be interpreted as environmental moni…
Decoherence Implies Information Gain
Dorje C. Brody, Lane P. Hughston
It is shown that if the wave function of a quantum system undergoes an arbitrary random transformation such that the diagonal elements of the density matrix in the decoherence basi…
Lévy Models for Collapse of the Wave Function
Dorje C. Brody, Lane P. Hughston
Recently there has been much progress in the development of stochastic models for state reduction in quantum mechanics. In such models, the collapse of the wave function is a physi…
PT symmetry and the evolution speed in open quantum systems
Dorje C. Brody
The dynamics of an open quantum system with balanced gain and loss is not described by a PT-symmetric Hamiltonian but rather by Lindblad operators. Nevertheless the phenomenon of P…
Higher-order uncertainty bounds for mixed states
Alex J. Belfield, Dorje C. Brody
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the H…
Quantum Measurement of Space-Time Events
Dorje C. Brody, Lane P. Hughston
The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the futu…
Evolution speed of open quantum dynamics
Dorje C Brody, Bradley Longstaff
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obta…
Making sense of the divergent series for reconstructing a Hamiltonian from its eigenstates and eigenvalues
Carl M. Bender, Dorje C. Brody, Matthew F. Parry
In quantum mechanics the eigenstates of the Hamiltonian form a complete basis. However, physicists conventionally express completeness as a formal sum over the eigenstates, and thi…
Comment on 'Comment on "Hamiltonian for the zeros of the Riemann zeta function" '
Carl M. Bender, Dorje C. Brody, Markus P. Müller
This paper is in response to a recent comment by Bellissard [arXiv:1704.02644] on the paper [Phys. Rev. Lett. 118, 130201 (2017)]. It is explained that the issues raised in the com…
Quantum State Reduction
Dorje C. Brody, Lane P. Hughston
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reductio…
Hamiltonian for the zeros of the Riemann zeta function
Carl M. Bender, Dorje C. Brody, Markus P. Müller
A Hamiltonian operator is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the no…
Consistency of PT-symmetric quantum mechanics
Dorje C. Brody
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here…
Universal Quantum Measurements
Dorje C. Brody, Lane P. Hughston
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional…
Fragile entanglement statistics
Dorje C. Brody, Lane P. Hughston, David M. Meier
If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical…
Time-optimal navigation through quantum wind
Dorje C. Brody, Gary W. Gibbons, David M. Meier
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the infl…
Elementary solution to the time-independent quantum navigation problem
Dorje C. Brody, David M. Meier
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realises a required quantum process or task, under the influence of a prevailing `backgr…
Solution to the quantum Zermelo navigation problem
Dorje C. Brody, David Meier
The solution to the problem of finding a time-optimal control Hamiltonian to generate a given unitary gate, in an environment in which there exists an uncontrollable ambient Hamilt…
Thermodynamics of Quantum Heat Bath
Dorje C. Brody, Lane P. Hughston
A model for the thermodynamics of a quantum heat bath is introduced. Under the assumption that the bath molecules have finitely many degrees of freedom and are weakly interacting,…
Biorthogonal Quantum Mechanics
Dorje C. Brody
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class…
Information Geometry of Complex Hamiltonians and Exceptional Points
Dorje C. Brody, Eva-Maria Graefe
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eige…
Mixed-state evolution in the presence of gain and loss
Dorje C. Brody, Eva-Maria Graefe
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked…