Results 1 - 10 of 7966
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[en] Formulation of modular theory for weakly closed J-involutive algebras of bounded operators in Pontryagin spaces is continued. Spectrum of the modular operator of such an algebra is investigated in detail. The existence of strongly continuous J-unitary group is established and Tomita's fundamental theorem is proved under the assumption that the spectrum of Δ belongs to the right half-plane
[en] In this paper they discuss some topics related to the general theory of frames. In particular, they focus their attention to the existence of different ''reconstruction formulas'' for a given vector of a certain Hilbert space and to some refinement of the perturbative approach for the computation of the dual frame
[en] The paper is concerned with solutions of Cauchy's problem for stochastic differential-operator equations in separable Hilbert spaces. Special emphasis is placed on the case when the operator coefficient of the equation is not a generator of a C0-class semigroup, but rather generates some regularized semigroup. Regularized solutions of equations in the Itô form with a Wiener process as an inhomogeneity and generalized solutions of equations with white noise are constructed in various spaces of abstract distributions. Bibliography: 23 titles.
[en] Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function (WF) does not work for these systems. In this paper we show that in order to let WF satisfy a *-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a *-Exponential expansion in deformation quantization.
[en] A deterministic multiparty quantum secret sharing scheme is put forward, in which Bell states in high-dimensional Hilbert space are used. Only by preforming High-dimensional Bell measurements, all agents can recover the secret according to the dealer’s announcement when collaborating with each other. It shows that unitary operation for encoding deterministic secret is unnecessary in quantum communication. The security of the transmission of the high-dimensional Bell states can be ensured by randomly using one of the two mutually unbiased bases for eavesdropping checking, and thus by which the proposed quantum secret sharing scheme is secure against usual attacks. In addition, the proposed scheme has three advantages: generality, high resource capacity and high security.
[en] We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
[en] In this paper, we prove some new dynamic inequalities involving Hilbert and Hardy–Hilbert operators with kernels and use them to establish general forms of multiple Hilbert and Hardy–Hilbert type inequalities on time scales.
[en] The emergence of non-configurational symmetry is studied in a minimal example. The system under scrutiny consists of a dimeric hexagonal complex with configurational C 3 symmetry, formulated as a tight-binding model. An accidental three-fold degeneracy point in parameter space is found; it is shown that an internal symmetry group operates on Hilbert space, but not on configuration space. The corresponding discrete Wigner functions for the irreducible representations of are utilized to show that a phase space is sufficient to exhibit an invariant subset. The dynamical symmetry is thus identified with a discrete semi-plane. Some implications on other known hidden symmetries of continuous systems are qualitatively discussed. (paper)