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  4. Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach

Oct

17

Tuesday

Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach

3.00pm

Seminars

Staff, Students, Academics

Speaker: Apostolos Vourdas (Bradford)

Research Centre: Department of Mathematics

Title: Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach

Abstract:

A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a `generalized basis', which is practically useful. The dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses Moebius transforms. There is non-independence and redundancy in these generalized bases, which is quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases, are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coefficients. Also in a physical system with ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system.

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When & where

3.00pm - 4.00pmTuesday 17th October 2017

CLG54 Tait Building City, University of London Northampton Square London EC1V 0HB United Kingdom

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City, University of London

Northampton Square

London EC1V 0HB

United Kingdom

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City, University of London is an independent member institution of the University of London. Established by Royal Charter in 1836, the University of London consists of 18 independent member institutions with outstanding global reputations and several prestigious central academic bodies and activities.