Minimal number of operators for observability ofN-level quantum systems

This paper discusses the minimal numbern _min of operatorsA ₁,...,A _n , whose expectation values at some instants determine the statistical state of anN-level quantum system. We assume that the macroscopic information about the system in question is given by the mean values Tr[ρ(t _j )A _i ]=m _i (t _j ) ofn self-adjoint operatorsA ₁,...,A _n at some instantst ₁<t ₂t _s , wheres ²?1.     

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.     

A new description of dissipative systems in quantum statistical mechanics

A method has been developed permitting to find the solution of the Liouville equation of quantum statistical mechanics. Canonical distributions are derived.     

A new method for determining excited states of quantum systems

Summary A new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyE _t, we consider the auxiliary operatorA=(H−E _t)². We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

A new proof of the propagation theorem forN-body quantum systems

A new proof of I. Sigal's and A. Soffer's propagation theorem is given. This theorem describes a large class of operators which are Kato-smooth with respect to anN-body Schrödinger operator.On leave from Division of Mathematical Methods in Physics, Warsaw University, Hoza 74, PL-00682 Warsaw, Poland     

A new physical characterisation of classical systems in quantum mechanics

A physical characterisation of classical systems in quantum mechanics is given in terms of the set of ensembles in contrast to the well-known characterisations concerning the effects or observables: A quantum mechanical system is classical if and only if each two decompositions of every ensemble are compatible.     

A new quantum number in the description of 8Be

We introduce a schematic Hamiltonian to describe ⁸Be. A new quantum number emerges from a shell-model and configuration interaction calculation for this nucleus. The theoretical introduction of this quantum number is accounted for by a new classification of states in terms of the unitary irreducible representations of the non-compact group Sp(2, R). The classification of states is shown to be physically relevant.     

Asymptotic completeness forN-body short-range quantum systems: A new proof

We give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials. It relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories.Dedicated to Res Jost and Arthur Wightman     

A new boundary condition for simulations of systems with charge-charge interactions

We introduce a new boundary condition for simulation of charged systems which is a generalization of periodic boundary conditions and reduces the long-range correlations inherent in periodic boundary conditions. An effective pair potential is calculated for the new condition.     

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.     

A new approach to Ermakov systems and applications in quantum physics

Milne–Pinney equation [(x)\ddot]=-w²(t)x+ k/x³\ddot x=-\omega^2(t)x+ k/{x^3} is usually studied together with the time-dependent harmonic oscillator [(y)\ddot]+w²(t) y=0\ddot y+\omega^2(t) y=0 and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint.     

A new method of quantization of classical solutions

The stochastic quantization method of Parisi and Wu is used to derive exact equations for the correlators of quantum fluctuations around the classical solution in the massless φ ⁴ theory. The equations obtained are then solved in the lowest orders of perturbation theory, and the first correction to the free propagator of a quantum fluctuation is calculated. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 381–386 (10 March 1996) Publsihed in English in the original Russian journal. Edited by Steve Torstveit.     

A hybrid quantum encoding algorithm of vector quantization for image compression

Many classical encoding algorithms of vector quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45\sqrt{N} times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than \sqrt{N} for most images, and it is more efficient than the pure quantum algorithm.     

A new construction of quasi-solvable quantum many-body systems of deformed Calogero-Sutherland type

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M+1) module, and we thus call it type A′. We construct the most general quasi-solvable operator of (at most) second-order which preserves the type A′ space. Investigating directly the condition under which the type A′ operators can be transformed to Schrödinger operators, we obtain the complete list of the type A′ quasi-solvable quantum many-body systems. In particular, we find new quasi-solvable models of deformed Calogero-Sutherland type which are different from the Inozemtsev systems. We also examine a new multivariate generalization of the type C monomial space based on the type A′ scheme.     

Sp(2) BRST invariant quantization of strings: The harmonic gauge

We analyze the mixed algebra of local diffeomorphisms and Weyl transformations for bosonic strings. BRST and anti-BRST operators are then constructed keeping a manifest Sp(2) invariance. The harmonic gauge arises as a natural gauge choice. All this work is redone in the presence of a two-dimensional background metric. We manage to write down a simple action, to compute the stress tensor and to work out the critical dimensions.     

A new mathematical problem related to quantization of fields

This paper is a survey of author??s mathematical and logical studies concerning the quantization of fields.