Publications
165 results found
Brody DC, Hughston LP, 2023, Lévy models for collapse of the wave function, Journal of Physics A: Mathematical and Theoretical, Vol: 56, Pages: 125303-125303, ISSN: 1751-8113
<jats:title>Abstract</jats:title> <jats:p>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 physical process, governed by a nonlinear stochastic differential equation that generalizes the Schrödinger equation. The present paper considers energy-based stochastic extensions of the Schrödinger equation. Most of the work carried out hitherto in this area has been concerned with models where the process driving the stochastic dynamics of the quantum state is Brownian motion. Here, the Brownian framework is broadened to a wider class of models where the noise process is of the Lévy type, admitting stationary and independent increments. The properties of such models are different from those of Brownian reduction models. In particular, for Lévy models the decoherence rate depends on the overall scale of the energy. Thus, in Lévy reduction models, a macroscopic quantum system will spontaneously collapse to an eigenstate even if the energy level gaps are small.</jats:p>
Brody DC, 2022, Noise, Fake News, and Tenacious Bayesians, FRONTIERS IN PSYCHOLOGY, Vol: 13, ISSN: 1664-1078
Brody DC, 2022, Open quantum dynamics for plant motions, SCIENTIFIC REPORTS, Vol: 12, ISSN: 2045-2322
Belfield AJ, Brody DC, 2021, Higher-order uncertainty bounds for mixed states, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 54, ISSN: 1751-8113
Brody DC, 2021, PT symmetry and the evolution speed in open quantum systems, Journal of Physics: Conference Series, Vol: 2038, ISSN: 1742-6588
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 PT-symmetry breaking and the impact of exceptional points can be observed in the Lindbladean dynamics. Here we briefly review the development of PT symmetry in quantum mechanics, and the characterisation of PT-symmetry breaking in open quantum systems in terms of the behaviour of the speed of evolution of the state.
Brody DC, Hughston LP, 2021, Quantum measurement of space-time events, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 54, ISSN: 1751-8113
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- Citations: 2
Bender CM, Brody DC, Parry MF, 2020, Making sense of the divergent series for reconstructing a Hamiltonian from its eigenstates and eigenvalues, Publisher: AMER INST PHYSICS
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- Citations: 3
Brody D, Hughston L, Meister B, 2020, Theory of Cryptocurrency Interest Rates, Publisher: SIAM PUBLICATIONS
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- Citations: 1
Brody DC, 2019, Modelling election dynamics and the impact of disinformation
Complex dynamical systems driven by the unravelling of information can be modelled effectively by treating the underlying flow of information as the model input. Complicated dynamical behaviour of the system is then derived as an output. Such an information-based approach is in sharp contrast to the conventional mathematical modelling of information-driven systems whereby one attempts to come up with essentially ad hoc models for the outputs. Here, dynamics of electoral competition is modelled by the specification of the flow of information relevant to election. The seemingly random evolution of the election poll statistics are then derived as model outputs, which in turn are used to study election prediction, impact of disinformation, and the optimal strategy for information management in an election campaign.
Brody DC, Longstaff B, 2019, Evolution speed of open quantum dynamics, Publisher: AMER PHYSICAL SOC
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- Citations: 16
Bender CM, Brody DC, 2019, Operator-valued zeta functions and Fourier analysis, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 52, ISSN: 1751-8113
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- Citations: 1
Brody DC, 2018, Biorthogonal systems on unit interval and zeta dilation operators, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 51, ISSN: 1751-8113
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- Citations: 2
Brody DC, Hughston LP, Meier DM, 2018, LEVY-VASICEK MODELS AND THE LONG-BOND RETURN PROCESS, Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD, ISSN: 0219-0249
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- Citations: 1
, 2018, Collapse of the Wave Function, Publisher: Cambridge University Press, ISBN: 9781108428989
Bender CM, Brody DC, 2018, Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 51, ISSN: 1751-8113
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- Citations: 4
Brody DC, Hughston LP, 2018, SOCIAL DISCOUNTING AND THE LONG RATE OF INTEREST, MATHEMATICAL FINANCE, Vol: 28, Pages: 306-334, ISSN: 0960-1627
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- Citations: 6
Brody DC, Hughston LP, 2018, Quantum State Reduction, Pages: 47-73
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 reduction have considered stochastic extensions of the Schrödinger equation, and have introduced the density matrix as the expectation of the random pure projection operator associated with the evolving state vector. After working out properties of the reduction process, we construct a general solution to the energydriven stochastic master equation. The solution is obtained by the use of nonlinear filtering theory and takes the form of a completely positive stochastic map.
Brody DC, 2017, PT-symmetry, indefinite metric, and nonlinear quantum mechanics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 50, ISSN: 1751-8113
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- Citations: 5
Bender CM, Brody DC, Mueller MP, 2017, Hamiltonian for the Zeros of the Riemann Zeta Function, PHYSICAL REVIEW LETTERS, Vol: 118, ISSN: 0031-9007
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- Citations: 52
Brody DC, Hughston LP, 2016, Thermodynamics of quantum heat bath, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 49, ISSN: 1751-8113
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- Citations: 4
Brody DC, Gibbons GW, Meier DM, 2016, A Riemannian approach to Randers geodesics, JOURNAL OF GEOMETRY AND PHYSICS, Vol: 106, Pages: 98-101, ISSN: 0393-0440
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- Citations: 5
Brody DC, 2016, Consistency of PT-symmetric quantum mechanics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 49, ISSN: 1751-8113
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- Citations: 51
Bender CM, Brody DC, Hughston LP, et al., 2016, Geometric Aspects of Space-Time Reflection Symmetry in Quantum Mechanics, 15th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP), Publisher: SPRINGER-VERLAG BERLIN, Pages: 185-199, ISSN: 0930-8989
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- Citations: 1
, 2016, Non-Hermitian Hamiltonians in Quantum Physics, Publisher: Springer International Publishing, ISBN: 9783319313542
Brody DC, Hughston LP, Meier DM, 2015, Fragile entanglement statistics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113
Brody DC, Law YT, 2015, Pricing of Defaultable Bonds with Random Information Flow, Applied Mathematical Finance, Vol: 22, Pages: 399-420, ISSN: 1350-486X
In the information-based approach to asset pricing, the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market then determines the overall magnitude of asset volatility. By letting this information flow rate random, we obtain an elementary stochastic volatility model within the information-based approach. Such an extension is justified on account of the fact that in real markets information flow rates are rarely measurable. Effects of having a random information flow rate are investigated in detail in the context of a simple model setup. Specifically, the price process of an elementary defaultable bond is derived, and its characteristic behaviours are revealed via simulation studies. The price of a European-style option on the bond is worked out, showing that the model has a sufficient flexibility to fit volatility surface. As an extension of the random information flow model, modelling of price manipulation is considered. A simple model is used to show how the skewness of the manipulated and unmanipulated price processes take opposite signature.
Brody DC, Hadjipetri S, 2015, COHERENT CHAOS INTEREST-RATE MODELS, INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, Vol: 18, ISSN: 0219-0249
Brody DC, Gibbons GW, Meier DM, 2015, Time-optimal navigation through quantum wind, NEW JOURNAL OF PHYSICS, Vol: 17, ISSN: 1367-2630
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- Citations: 39
Brody DC, Meier DM, 2015, Solution to the Quantum Zermelo Navigation Problem, PHYSICAL REVIEW LETTERS, Vol: 114, ISSN: 0031-9007
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- Citations: 33
Brody DC, Meier DM, 2015, Elementary solution to the time-independent quantum navigation problem, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113
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- Citations: 13
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