27,722 research outputs found
Entanglement Induced Phase Transitions
Starting from the canonical ensemble over the space of pure quantum states,
we obtain an integral representation for the partition function. This is used
to calculate the magnetisation of a system of N spin-1/2 particles. The results
suggest the existence of a new type of first order phase transition that occurs
at zero temperature in the absence of spin-spin interactions. The transition
arises as a consequence of quantum entanglement. The effects of internal
interactions are analysed and the behaviour of the magnetic susceptibility for
a small number of interacting spins is determined.Comment: 4 pages, 2 figure
Elementary solution to the time-independent quantum navigation problem
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realizes a required quantum process or task, under the influence of a prevailing ‘background’ Hamiltonian that cannot be manipulated. When the task is to transform one quantum state into another, finding the solution in closed form to the problem is nontrivial even in the case of timeindependent Hamiltonians. An elementary solution, based on trigonometric analysis, is found here when the Hilbert space dimension is two. Difficulties arising from generalizations to higher-dimensional systems are discussed
The Wagner Act and the Question of Workplace Representation
Paper_Brody_011094.pdf: 2455 downloads, before Oct. 1, 2020
Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints
Constrained quantum dynamics is used to propose a nonlinear dynamical
equation for pure states of a generalized coarse-grained system. The relevant
constraint is given either by the generalized purity or by the generalized
invariant fluctuation, and the coarse-grained pure states correspond to the
generalized coherent i.e. generalized nonentangled states. Open system model of
the coarse-graining is discussed. It is shown that in this model and in the
weak coupling limit the constrained dynamical equations coincide with an
equation for pointer states, based on Hilbert-Schmidt distance, that was
previously suggested in the context of the decoherence theory
Disambiguating Different Covariation Types
Covariations in neuronal latency or excitability can lead to peaks in spike train covariograms that may be very similar to those caused by spike timing synchronization (see companion article). Two quantitative methods are described here. The first is a method to estimate the excitability component of a covariogram, based on trial-by-trial estimates of excitability. Once estimated, this component may be subtracted from the covariogram, leaving only other types of contributions. The other is a method to determine whether the covariogram could potentially have been caused by latency covariations
Biorthogonal systems on unit interval and zeta dilation operators
An elementary 'quantum-mechanical' derivation of the conditions for a system
of functions to form a Reisz basis of a Hilbert space on a finite interval is
presented.Comment: 4 pages, 1 figur
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 {\it 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.Comment: 20 pages, 5 figure
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