Stochastic sequential reduction of commutative Hamiltonians

Name: Stochastic sequential reduction of commutative Hamiltonians
Author: Mengütürk, L. A., Mengütürk, Murat Cahit

İsim	Stochastic sequential reduction of commutative Hamiltonians
Yazar	Mengütürk, L. A., Mengütürk, Murat Cahit
Basım Tarihi:	2020-10-01
Basım Yeri	- AIP Publishing
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0022-2488
Kayıt Numarası	acfd1dca-16b2-4756-bdd3-690c5a6ef989
Lokasyon	Business Administration
Tarih	2020-10-01
Örnek Metin	This paper introduces a class of stochastic processes constructed by conditioning cadlag processes to take a predetermined set of marginal laws at fixed points in time. We collectively refer to the elements of this class of processes as random n-bridges (RnBs), where n refers to the cardinality of the set of conditioning laws, which can be chosen arbitrarily. We prove that if the underlying cadlag process is Markov, then its RnB is Markov for n = 1 and has a particular Markov-like property for n > 1. As a canonical subclass, we construct Brownian RnBs (BRnBs) and provide their anticipative representation as well as their non-anticipative semimartingale representation. This motivates the second part of this paper, wherein we apply BRnBs to describe an energy-based state reduction in a composite quantum system involving a set of commuting observables measured successively at different times. The highly tractable so-called energy-based quantum state reduction models are significant in their role as the most important alternative to the popular CLS model. We ask the random variables composing the anticipative form of a BRnB to take the eigenvalues of a set of compatible Hamiltonians and provide a new stochastic Schrodinger evolution on a complex Hilbert space that models sequential reduction dynamics of the eigenstates through a single wave function. By doing so, we also extend the Brody-Hughston finite-time collapse model to a many-body setup with sequential measurements.
DOI	10.1063/5.0004810
Cilt	61

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Stochastic sequential reduction of commutative Hamiltonians

Yazar Mengütürk, L. A., Mengütürk, Murat Cahit

Basım Tarihi 2020-10-01

Basım Yeri - AIP Publishing

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0022-2488

Kayıt Numarası acfd1dca-16b2-4756-bdd3-690c5a6ef989

Lokasyon Business Administration

Tarih 2020-10-01

Örnek Metin This paper introduces a class of stochastic processes constructed by conditioning cadlag processes to take a predetermined set of marginal laws at fixed points in time. We collectively refer to the elements of this class of processes as random n-bridges (RnBs), where n refers to the cardinality of the set of conditioning laws, which can be chosen arbitrarily. We prove that if the underlying cadlag process is Markov, then its RnB is Markov for n = 1 and has a particular Markov-like property for n > 1. As a canonical subclass, we construct Brownian RnBs (BRnBs) and provide their anticipative representation as well as their non-anticipative semimartingale representation. This motivates the second part of this paper, wherein we apply BRnBs to describe an energy-based state reduction in a composite quantum system involving a set of commuting observables measured successively at different times. The highly tractable so-called energy-based quantum state reduction models are significant in their role as the most important alternative to the popular CLS model. We ask the random variables composing the anticipative form of a BRnB to take the eigenvalues of a set of compatible Hamiltonians and provide a new stochastic Schrodinger evolution on a complex Hilbert space that models sequential reduction dynamics of the eigenstates through a single wave function. By doing so, we also extend the Brody-Hughston finite-time collapse model to a many-body setup with sequential measurements.

DOI 10.1063/5.0004810

Cilt 61