Results 21  30
of
103
Local dynamics of meanfield Quantum Systems
, 1991
"... . In this paper we extend the theory of meanfielddynamical semigroups given in [DW1,Du1] to treat the irreversible meanfield dynamics of quasilocal meanfield observables. These are observables which are site averaged except within a region of tagged sites. In the thermodynamic limit the tagged ..."
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Cited by 6 (1 self)
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. In this paper we extend the theory of meanfielddynamical semigroups given in [DW1,Du1] to treat the irreversible meanfield dynamics of quasilocal meanfield observables. These are observables which are site averaged except within a region of tagged sites. In the thermodynamic limit the tagged sites absorb the whole lattice, but also become negligible in proportion to the bulk. We develop the theory in detail for a class of interactions which contains the meanfield versions of quantum lattice interactions with infinite range. For this class we obtain an explicit form of the dynamics in the thermodynamic limit. We show that the evolution of the bulk is governed by a flow on the oneparticle state space, whereas the evolution of local perturbations in the tagged region factorizes over sites, and is governed by a cocycle of completely positive maps. We obtain an Htheorem which suggests that local disturbances typically become completely delocalized for large times, and we show this...
Eigenvalue estimates for nonnormal matrices and the zeros of random orthogonal polynomials on the unit circle
 J. Approx. Theory
"... Abstract. We prove that for any n × n matrix, A, and z with z  ≥ �A�, we have that �(z − A) −1 � ≤ cot ( π 4n)dist(z, spec(A))−1. We apply this result to the study of random orthogonal polynomials on the unit circle. 1. ..."
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Cited by 6 (3 self)
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Abstract. We prove that for any n × n matrix, A, and z with z  ≥ �A�, we have that �(z − A) −1 � ≤ cot ( π 4n)dist(z, spec(A))−1. We apply this result to the study of random orthogonal polynomials on the unit circle. 1.
First Order Perturbations Of Dirichlet Operators: Existence And Uniqueness
, 1996
"... We study perturbations of type B \Delta r of Dirichlet operators (L 0 ; D(L 0 )) associated with Dirichlet forms of type E 0 (u; v) = 1=2 R hru; rviH d¯ on L 2 (E; ¯) where E is a finite or infinite dimensional Banach space E. Here H denotes a Hilbert space densely and continuously embed ..."
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Cited by 5 (1 self)
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We study perturbations of type B \Delta r of Dirichlet operators (L 0 ; D(L 0 )) associated with Dirichlet forms of type E 0 (u; v) = 1=2 R hru; rviH d¯ on L 2 (E; ¯) where E is a finite or infinite dimensional Banach space E. Here H denotes a Hilbert space densely and continuously embedded in E. Assuming quasiregularity of (E 0 ; D(E 0 )) we show that there always exists a closed extension of Lu := L 0 u + hB; ruiH that generates a subMarkovian C 0 semigroup of contractions on L 2 (E; ¯) (resp. L 1 (E; ¯)), if B 2 L 2 (E; H;¯) and R hB; ruiH d¯ 0; u 0. If D is an appropriate core for (L 0 ; D(L 0 )) we show that there is only one closed extension of (L; D) in L 1 (E; ¯) generating a strongly continuous semigroup. In particular we apply our results to operators of type \Delta H +B \Delta r, where \Delta H denotes the GrossLaplacian on an abstract Wiener space (E; H; fl) and B = \Gammaid E + v, where v takes values in the CameronMartin s...
Quantum feedback networks: Hamiltonian formulation,” 2008, to appear
 The Australian National University
, 2007
"... A quantum network is an open system consisting of several component Markovian inputoutput subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we formulate the model description by prescribing the Hamiltonian for ..."
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Cited by 5 (3 self)
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A quantum network is an open system consisting of several component Markovian inputoutput subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we formulate the model description by prescribing the Hamiltonian for the network including details the component systems, the field channels, their interconnections, interactions and any time delays arising from the geometry of the network. The model is nonMarkovian for finite time delays, but in the limit where these delays vanish we recover a Markov model and thereby deduce the rules for introducing feedback into arbitrary quantum networks. The type of feedback considered includes that mediated by the use of beam splitters. We are therefore able to give a systemtheoretic approach to introducing connections between quantum mechanical statebased inputoutput systems, and give a unifying treatment using noncommutative fractional linear, or Möbius, transformations.
New Spectral Criteria for Almost Periodic Solutions of Evolution Equations
"... We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form x = A(t)x+f(t) (), with f having precompact range, which will be then applied to find new spectral criteria for the existence of almost periodic solutions ..."
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Cited by 5 (3 self)
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We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form x = A(t)x+f(t) (), with f having precompact range, which will be then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonnant case where e isp(f) may intersect the spectrum of the monodromy operator P of () (here sp(f) denotes the Carleman spectrum of f ). We show that if () has a bounded uniformly continuous mild solution u and oe \Gamma (P )ne isp(f) is closed, where oe \Gamma (P ) denotes the part of oe(P ) on the unit circle, then () has a bounded uniformly continuous mild solution w such that e isp(w) = e isp(f) . Moreover, w is a "spectral component" of u. This allows to solve the general Masseratyped problem for almost periodic solutions. Various spectral criteria for the existence of almost periodic, quasiperiodic mild solutions to () are ...
SEMIGROUP GROWTH BOUNDS
, 2003
"... The theory of oneparameter semigroups provides a good entry into the study of the properties of nonselfadjoint operators and of the evolution equations associated with them. There are many situations in which such an operator A arises by linearizing some nonlinear evolution equation around a sta ..."
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Cited by 5 (1 self)
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The theory of oneparameter semigroups provides a good entry into the study of the properties of nonselfadjoint operators and of the evolution equations associated with them. There are many situations in which such an operator A arises by linearizing some nonlinear evolution equation around a stationary point. The stability
Sharp Bounds on Heat Kernels of Higher Order Uniformly Elliptic Operators
 J. Operator Theory
, 1996
"... this paper is to obtain precise quantitative bounds on the constants c 2 ..."
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Cited by 4 (1 self)
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this paper is to obtain precise quantitative bounds on the constants c 2
DISCRETE SPECTRUM AND ALMOST PERIODICITY
"... Abstract. The purpose of this note is to show that solutions of first and second order Cauchy problems with almost periodic inhomogeneity are almost periodic on the real line whenever the spectrum of the underlying operator is discrete. 1. ..."
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Cited by 4 (0 self)
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Abstract. The purpose of this note is to show that solutions of first and second order Cauchy problems with almost periodic inhomogeneity are almost periodic on the real line whenever the spectrum of the underlying operator is discrete. 1.
Defective Intertwining Property And Generator Domain
"... . We discuss the defective intertwining property of generators of semigroups. We give an equivalent conditions in terms of generator, resolvent and semigroup. As an application, using this property, we give a example that we can determine the exact generator domain of a Schrodinger operator. 1. Intr ..."
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Cited by 4 (4 self)
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. We discuss the defective intertwining property of generators of semigroups. We give an equivalent conditions in terms of generator, resolvent and semigroup. As an application, using this property, we give a example that we can determine the exact generator domain of a Schrodinger operator. 1. Introduction The intertw#rt]L property plays an important role to deal w#al semigroups. The intertw #A0(D property takes the follow#ll form: DA= AD w#1]( A and A are generators of semigroups and D is a closed operator. In the privious paper [8],w e discuss the intertw#rt]4 property and apply it to the issue of the domain of a generator. But there are many issuesw#su h are notw#t](F a scope of intertw#rt]) property. In this paper,w e extend it to the follow#ll defective intertw#rt]( property: DA = AD + R. Here, an additional term R appears. We discuss the equivalent conditions in terms of resolvents and semigroups. We formulate the issue in theframew ork of Banach space. In the case o...
Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces
, 1995
"... A principal result of the paper is that if E is a symmetric Banach function space on the positive halfline with the Fatou property then, for all semifinite von Neumann algebras (M; ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator space E(M; ) with Lipsch ..."
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Cited by 4 (0 self)
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A principal result of the paper is that if E is a symmetric Banach function space on the positive halfline with the Fatou property then, for all semifinite von Neumann algebras (M; ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator space E(M; ) with Lipschitz constant depending only on E if and only if E has nontrivial Boyd indices. It follows that if