On observability of N-level quantum systems

The purpose of this paper is to discuss necessary and sufficient conditions for observability of N-level quantum systems. We assume that the information about a physical system is given by the mean values Tr(?(t_j)A_i) = m_Ai(t_j), of n self-adjointoperators A₁,…,A_n on $\text{H}$ at some instants t₁ < t₂ <…<t_s. The question of theminimal number n of operators A₁,…,A_n (physical quantities $\text{A}{}_1\text{, …,}\text{A}{}_{\mathrm{n}}$) for which the quantum system $\text{S}$ is (A₁,…,A_n)-observableis discussed.     

The essential nonlinearity ofN-level quantum thermodynamics

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.     

Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or -symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity.     

Bounds on exponentials of local number operators in quantum statistical mechanics

We consider the quantum systems of interacting Bose particles confined to a bounded region of the configuration spaces ^v . For a class of superstable interactions we obtain bounds on exponentials of local number operators for any temperature and activity. The method we use is the Wiener integral formalism in statistical mechanics. As a consequence any thermodynamic limit states are entire analytic and locally normal in the CCR algebra. In some cases these are modular states.Research supported in part by a grant from Korean Science Foundation     

Does the quantum formalism allow for the observability of empty quantum waves?

The compatibility of the notion of empty wave with quantum mechanics is investigated. Invoking general physical requirements valid in quantum mechanics it is shown that a picture of a quantum system in terms of an empty wave and a non-empty wave containing a quantum particle is deficient. Research associate N.F.W.O. (Belgium).     

Assignment of quantum number for plasmon energies in carbon layer systems

Electron-emission distribution curves of carbon layer surfaces excited by primary electrons of energies in the 118-534 eV range have been measured. The first four peaks in the plasmon spectrum are observed. It is concluded that the oscillator energies are presented to explain the assignment of the quantum number (n = 0,1,2,3) for internal plasmons in carbon layer systems. The preliminary assignment is in good agreement with the experimental results. It is also shown that the existence of limit between internal and surface plasmons. It is pointed out that the plasmon energy does not depend on both the external electrostatic voltage and the sample temperature. Moreover, the quantum number was adopted to the names of internal plasmons in the observed spectra.     

On the direct observability of quantum waves

Fundamental experiments on the dual nature of atomic entities (photons, electrons, neutrons, etc.) can be interpreted in terms of empty waves not carrying energy and momentum. Similar points of view were advanced in famous papers by Einstein, de Broglie, Bohr, and Born. Recent proposals could lead to experimental tests of this idea, using low intensity photon beams, thanks to modern experimental apparatuses.     

Tensor operators for quantum algebras

Tensor operators are discussed for Hopf algebras and, in particular, for a quantum (q-deformed) algebraUq(g), whereg is any simple finite-dimensional or affine Lie algebra. These operators are defined via an adjoint action in a Hopf algebra. There are two types of the tensor operators which correspond to two coproducts in the Hopf algebra. In the case of tensor products of two tensor operators one can obtain 8 types of the tensor operators and so on. We prove the relations which can be a basis for a proof of the Wigner-Eckart theorem for the Hopf algebras. It is also shown that in the case ofUq(g) a scalar operator can be differed from an invariant operator but atq=1 these operators coincide. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163, and by INTAS-00-00055.     

Onq-tensor operators for quantum groups

The fundamental theorem for tensor operators in quantum groups is proved using an appropriate definition forq-tensor operators. An example is discussed based on theq-boson realization of SU _q (2).Supported in part by the Department of Energy.     

Time operators for quantum walks

Letters in Mathematical Physics - We study time operators for discrete-time quantum systems. Quantum walks are typical examples. We construct time operators for one-dimensional homogeneous quantum...     

角动量量子数l的升降算符和球谐函数的生成

1999年喀兴林先生在<高等量子力学>一书中首次提出角动量量子数l的升降算符,这个算符其实是一秩不可约张量算符的一个简单实现.当给定一个磁量子数m,降算符能给出最小量子数l的状态,进而得到全部球谐函数的最低态|0,0>.而通过升降算符的恰当组合,作用在这个最低态上就可以生成任意球谐函数|lm>.     

Phase space propagators for quantum operators

The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier transform, the chord representation are, respectively, unitary reflection and translation operators. Thus, the general semiclassical study of unitary operators allows us to propagate arbitrary operators, including density operators, i.e., the Wigner function. The various propagation kernels are different representations of the super-operators which act on the space of operators of a closed quantum system. We here present the mixed semiclassical propagator, that takes translation chords to reflection centres, or vice versa. In contrast to the centre-centre propagator that directly evolves Wigner functions, they are guaranteed to be caustic free, having a simple WKB-like universal form for a finite time, whatever the number of degrees of freedom. Special attention is given to the near-classical region of small chords, since this dominates the averages of observables evaluated through the Wigner function.     

Construction of quantum operators

On the basis of an analysis of the existing methods of constructing quantum operators, requirements are formulated for a correspondence principle that is free from the defects of the familar principles. It is shown that such a principle exists. Its explicit form is determined and the properties of the resulting operators are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 102–106, November, 1971.The author wishes to thank Professor Ya. P. Terletskii and the participants in the theoretical seminar at the University of International Friendship for their valuable comments.     

Selective control of the states of multilevel quantum systems using nonselective rotation operators

We have calculated the sequences of nonselective rotation operators separated by intervals of free evolution that perform selective rotations between adjacent levels in systems with three, four, five, and six nonequidistant levels. We have numerically simulated the realization of the calculated sequences for quadrupole nuclei with corresponding spins controlled by intense nonselective radio-frequency (RF) pulses and investigated the dependences of the realization error on the parameters of external and internal interactions. To reduce the error when the RF field is not strong enough, we have found composite nonselective RF pulses consisting of five simple ones. We show that the error of the composite selective rotation operator can be reduced signifi- cantly in comparison to the error of a simple single selective pulse.     

Absence of wave operators for one-dimensional quantum walks

Letters in Mathematical Physics - We show that there exist pairs of two time evolution operators which do not have wave operators in a context of one-dimensional discrete time quantum walks. As a...     

Application of partial observability for analysis and design of synchronized systems

Synchronization in identical drive-response systems is a problem that can be cast in an observer design framework. In this paper we extend this approach by studying the analysis/design of partial synchronization by means of observer theory. In doing so, we introduce the concept of partial observer--an observer to reconstruct a part of the system state vector. It is also shown how the observability condition can be utilized to analyze the dynamics in an array of coupled identical systems.     

Heisenberg picture operators in the stochastic wave function approach to open quantum systems

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which “unravels” the quantum Master equation can be used for the calculation of matrix elements of reduced Heisenberg picture operators, and thus for the calculation of multitime correlation functions, by extending the stochastic process to a doubled Hilbert space. The numerical performance of the stochastic simulation algorithm is investigated by means of a standard example. Received: 30 May 1997 / Revised: 4 November 1997 / Accepted: 7 November 1997     

Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.     

Gates for quantum computing induced from monodromy operators

The monodromy approach to quantum computing is based on a holomorphic vector bundle with a meromorphic connection. The gates for computation are obtained from the monodromy matrices of the connection. The text was submitted by the author in English.     

Minimal quantum logic with merged implications

It is shown that the property of orthomodularity can be interpreted as a particular reduction of the operations of implication to the relation of implication, and a physical interpretation of the result is given.