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1.
The standard objects of quantum integrable systems are identified with elements of classical nonlinear integrable difference
equations. The functional relation for commuting quantum transfer matrices of quantum integrable models is shown to coincide
with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical
2D Toda lattice with open boundaries. Elliptic solutions of Hirota's equation give a complete set of eigenvalues of the quantum
transfer matrices. Eigenvalues of Baxter's Q-operator are solutions to the auxiliary linear problems for classical Hirota's equation. The elliptic solutions relevant
to the Bethe ansatz are studied. The nested Bethe ansatz equations for A
k-1
-type models appear as discrete time equations of motions for zeros of classical τ-functions and Baker-Akhiezer functions.
Determinant representations of the general solution
to bilinear discrete Hirota's equation are analysed and a new determinant formula for eigenvalues of the quantum transfer
matrices is obtained. Difference equations for eigenvalues of the Q-operators which generalize Baxter's three-term T− Q-relation are derived.
Received: 15 May 1996 / Accepted: 25 November 1996 相似文献
2.
It is shown that if one incorporates the generalized coordinate quantum velocities Q
1 as given by Q
1= l[ H,Q
1](h=1) into the generalized classical Lagrangian for a free particle (the total energy), L=1/2 Q
1
g
tk
Q
k one does not obtain (no matter what ordering of the operators q
l
, q
k
and g
lkwe choose the correct quantum Lagrangian operator which is a transformation from -1/2V 2 to generalized coordinates (Gruber, 1971, 1972). q
l as given by q
l=i[ H, q
l] turns out to be the Hermitian part of a more generaiized operator which we call the total generalized velocity operator similar to the notation in ear previous articles (Gruber, 1971, 1972). This total velocity operator really determines the fundamental structure governing our system in the Lagrangian formulation. We show that ft is through the total velocity operator that we make the transition from classical to quantum mechanics and through our procedure we arrive at the correct quantum Lagrangian operator. 相似文献
3.
We consider fermionic lattice systems with Hamiltonian H= H
{(0)}+λ H
Q
, where H
{(0)} is diagonal in the occupation number basis, while H
Q
is a suitable “quantum perturbation”. We assume that H
{(0)} is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitations, while H
Q
is a finite range or exponentially decaying Hamiltonian that can be written as a sum of even monomials in the fermionic creation
and annihilation operators. Mapping the d dimensional quantum system onto a classical contour system on a d+1 dimensional lattice, we use standard Pirogov–Sinai theory to show that the low temperature phase diagram of the quantum
system is a small perturbation of the zero temperature phase diagram of the classical
system, provided λ is sufficiently small. Particular attention is paid to the sign problems arising from the fermionic nature
of the quantum particles.
As a simple application of our methods, we consider the Hubbard model with an additional nearest neighbor repulsion. For this
model, we rigorously establish the existence of a paramagnetic phase with commensurate staggered charge order for the narrow
band case at sufficiently low temperatures.
Received: 23 December 1996/ Accepted: 7 April 1999 相似文献
4.
The consistent treatment of anticommuting parameters in quantum theories requires the introduction of the Hilbert Q module with a Q scalar product (where Q is infinite-dimensional Grassman-Banach algebra). The extended GNS construction for representations of Q algebras on such Q modules is given. 相似文献
5.
The problem of hidden variables in quantum mechanics is formalized as follows. A general or contextual (noncontextual) hidden-variables theory is defined as a mapping f: Q×M C (f: QC) where Q is the set of projection operators in the appropriate (quantum) Hilbert space, M is the set of maximal Boolean subalgebras of Q and C is a (classical) Boolean algebra. It is shown that contextual (noncontextual) hidden-variables always exist (do not exist). 相似文献
6.
The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q0 (Q0 is the initial width of the potential), the force is repulsive, and for Q > Q0, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field. 相似文献
7.
The transverse Ising Model (TIM) in one dimension is the simplest model which exhibits a quantum phase transition (QPT). Quantities
related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity are known to provide
signatures of QPTs. The issue is less well explored when the quantum system is subjected to decoherence due to its interaction,
represented by a quantum channel, with an environment. In this paper we study the dynamics of the mutual information I( ρ
AB
), the classical correlations C( ρ
AB
) and the quantum correlations Q( ρ
AB
), as measured by the QD, in a two-qubit state the density matrix of which is the reduced density matrix obtained from the
ground state of the TIM in 1d. The time evolution brought about by system-environment interactions is assumed to be Markovian
in nature and the quantum channels considered are amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum
channel is shown to be distinguished by a specific type of dynamics. In the case of the phase-flip channel, there is a finite
time interval in which the quantum correlations are larger in magnitude than the classical correlations. For this channel
as well as the bit-phase-flip channel, appropriate quantities associated with the dynamics of the correlations can be derived
which signal the occurrence of a QPT. 相似文献
8.
Relationship is established between the security of the BB84 quantum key distribution protocol and the forward and converse coding theorems for quantum communication channels. The upper bound Q c ≈ 11% on the bit error rate compatible with secure key distribution is determined by solving the transcendental equation $H(Q_c ) = \bar C(\rho )/2$ , where ρ is the density matrix of the input ensemble, $\bar C(\rho )$ is the classical capacity of a noiseless quantum channel, and H( Q) is the capacity of a classical binary symmetric channel with error rate Q. 相似文献
10.
A procedure is offered for evaluating the forces between classical, charged solitons at large distances. This is employed
for the solitons of a complex, scalar two-dimensional field theory with a U(1) symmetry, that leads to a conserved charge Q. These forces are the analogues of the strong interaction forces. The potential, U( Q, R), is found to be attractive, of long range, and strong when the coupling constants in the theory are small. The dependence
of U( Q, R) on Q, the sum of the charges of the two interacting solitons ( Q will refer to isospin in the SU(2) generalisation of the U(1) symmetric theory) is of importance in the theory of strong
interactions; group theoretical considerations do not give such information. The interaction obtained here will be the leading
term in the corresponding quantum field theory when the coupling-constants are small. 相似文献
11.
The concept of separation of procedures and the ST-transformation are briefly reviewed together with the equivalence theorem that a d-dimensional quantum system with finite-range interactions is equivalent to the corresponding ( d+1)-dimentional classical system with finite-range interactions. This theorem yields the introduction of the quantum transfer-matrix method. Thermo quantum dynamics is formulated using the quantum transfer-matrix method. This new formulation has the great merit that the thermal average Q for any observable Q in the thermodynamic limit is expressed as an expectation value over a temperature-dependent state vector in the single (conjugate) Hilbert space in the contrast to the usage of the double Hilbert space in thermo field dynamics. 相似文献
12.
We derive a classical integral representation for the partition function, Z
Q
, of a quantum spin system. With it we can obtain upper and lower bounds to the quantum free energy (or ground state energy) in terms of two classical free energies (or ground state energies). These bounds permit us to prove that when the spin angular momentum J (but after the thermodynamic limit) the quantum free energy (or ground state energy) is equal to the classical value. In normal cases, our inequality is Z
C
( J) Z
Q
( J) Z
C
( J+1).On leave from the Department of Mathematics, M.I.T., Cambridge, Mass. 02139, USA. Work partially supported by National Science Foundation Grant GP-31674X and by a Guggenheim Memorial Foundation Fellowship. 相似文献
13.
We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T– Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete quantum pendulum and discrete sine-Gordon model are our main concern in this report. By the quantum inverse scattering method, the Baxter's T– Q relation is formulated on the associated spectral curve, a high genus Riemann surface in general, arisen from the study of spectrum problem of the system. In the case of degenerated spectral curve where the spectral variables lie on rational curves, we obtain the complete and explicit solution of the T– Q polynomial equation associated to the model, and the intimate relation between the Baxter's T– Q relation and algebraic Bethe Ansatz is clearly revealed. The algebraic geometry of a general spectral curve attached to the model and certain qualitative properties of solutions of the Baxter's T– Q relation are discussed incorporating the physical consideration. 相似文献
14.
The EPR experiment is investigated within the abstract language of relativistic quantum physics (relativistic quantum logic). First we show that the principles of reality ( R) and locality ( L) contradict the validity principle ( Q) of quantum physics. A reformulation of this argument is then given in terms of relativistic quantum logic which is based on the principles R and Q. It is shown that the principle L must be replaced by a convenient relaxation ¯ L, by which the contradiction can be eliminated. On the other hand this weak locality principle ¯ L does not contradict Einstein causality and is thus in accordance with special relativity. 相似文献
15.
A general class of time evolutions
Q
of infinite quantum systems is rigorously defined. It generalizes thermodynamic limits of polynomial mean-field evolution of quantum spin lattices, the simplest case of which is the strong coupling version of the quasi spin B.C.S.-model of superconductivity. A distinguished feature of the considered type of time evolution is the
Q
-non-invariance of the usually considered C
*-algebra A of quasilocal observables of the infinite system. A larger C
*-algebra C containing A as a subalgebra is introduced in such a way that
Q
has a natural extension to a one parameter group *-automorphisms of C. The algebra C contains a commutative subalgebra of classical observables (consisting of the intensive observables of the large quantal system determined by a Lie group G action (G) *-aut A) denoted by N which is
Q
invariant and the restriction of
Q
to N reproduces the classical Hamiltonian flow
Q
corresponding to the chosen classical Hamiltonian function Q on the classical phase space of the intensive observables. The evolution
Q
is determined uniquely by the classical Hamiltonian function Q as well as by the action (G). Continuity properties of
Q
are considered and reviewed.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986. 相似文献
16.
We compute quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C for spin pairs at any distance in the infinite XY spin-1/2 chains, i.e., the anisotropic XY model and the isotropic XY model with three-spin interactions. We obtain two simple dominance relations: C ≥ E and D ≥ E + Q Except this, there are no other simple ordering relations between them. We also show that Q can detect the special points of the system where the entanglement just appears or completely disappears. In addition, it is worthwhile to mention that dissonance and classical correlation can also clearly spotlight the critical points of quantum phase transitions in XY spin-1/2 chains. 相似文献
17.
We compute the quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C in the eight-qubit XXZ spin-1/2 chain at finite temperatures. We find that not only D but also Q and C can clearly detect the critical points associated to quantum phase transitions for this model at finite temperatures. Moreover, Q can detect the special points of the system where the entanglement just appears or completely vanishes. Finally, we obtain two simple dominance relations: C≥ E and D≥ E+ Q. Except these there are no other simple ordering relations in this model. 相似文献
18.
We present several efficient entanglement concentration protocols (ECPs) with the nitrogen-vacancy (N-V) centers coupled to low- Q microresonators. Based on the input-output process of ancillary coherent light pulse in low- Q microresonators, we can obtain the maximally entangled states among remote participants via local operations and classical communication. Our protocols use a conventional photon detector to discriminate the two coherent states | α〉 and |? α〉, which is more convenient than homodyne measurement. We discuss the feasibility of our protocols, and they may be beneficial for quantum repeaters and quantum information processing. 相似文献
20.
The technique based on a *-algebra of Wick products of field operators in curved spacetime, in the local covariant version
proposed by Hollands and Wald, is strightforwardly generalized in order to define the stress-energy tensor operator in curved
globally hyperbolic spacetimes. In particular, the locality and covariance requirement is generalized to Wick products of
differentiated quantum fields. Within the proposed formalism, there is room to accomplish all of the physical requirements
provided that known problems concerning the conservation of the stress-energy tensor are assumed to be related to the interface
between the quantum and classical formalism. The proposed stress-energy tensor operator turns out to be conserved and reduces
to the classical form if field operators are replaced by classical fields satisfying the equation of motion. The definition
is based on the existence of convenient counterterms given by certain local Wick products of differentiated fields. These
terms are independent from the arbitrary length scale (and any quantum state) and they classically vanish on solutions of
the Klein-Gordon equation. Considering the averaged stress-energy tensor with respect to Hadamard quantum states, the presented
definition turns out to be equivalent to an improved point-splitting renormalization procedure which makes use of the nonambiguous
part of the Hadamard parametrix only that is determined by the local geometry and the parameters which appear in the Klein-Gordon
operator. In particular, no extra added-by-hand term g
αβQ
and no arbitrary smooth part of the Hadamard parametrix (generated by some arbitrary smooth term `` ω
0
') are involved. The averaged stress-energy tensor obtained by the point-splitting procedure also coincides with that found
by employing the local ζ-function approach whenever that technique can be implemented.
Received: 24 September 2001/Accepted: 14 May 2002 Published online: 22 November 2002 相似文献
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