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1.
We develop a technique for the construction of integrable models with a 2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang–Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group
, with a matrix deformation parameter q
such that (q
)2 = q
2. The symmetry behind these models can also be interpreted as the tensor product of the (–1)-Weyl algebra by an extension of
q
(gl(N)) with a Cartan generator related to deformation parameter –1. 相似文献
2.
Unstructured Adiabatic Quantum Search 总被引:2,自引:0,他引:2
In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. We apply this method to the Grover's problem, i.e., searching a marked item in an unstructured database. Classically, the problem can be solved only in a running time of order O(N) (where N is the number of items in the database), whereas in the quantum model a speed up of order
has been obtained. We show that in the adiabatic quantum model, by a suitable choice of the time-dependent Hamiltonian, it is possible to do the calculation in constant time, independent of the the number of items in the database. However, in this case the initial time-complexity of
is replaced by the complexity of implementing the driving Hamiltonian. 相似文献
3.
Claudio Albanese 《Communications in Mathematical Physics》1996,178(3):527-540
Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order
for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO(
–1. 相似文献
4.
Nils A. Törnqvist 《Zeitschrift fur Physik C Particles and Fields》1994,61(3):525-537
A systematic study of possible deuteronlike twomeson bound states,deusons, is presented. Previous arguments that many such bound states may exist are elaborated with detailed arguments and numerical calculations including, in particular, the tensor potential. This tensor potential which is crucial for the deuteron binding is shown to be very important also in the mesonic case. Especially, in the pseudoscalar3
P
0 pseudoscalar-vector
and vector-vector
channels the important observation is made that the centrifugal barrier from theP-wave can be overcome by the 1/r
2 and 1/r
3 terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteronlike
and
composites bound by approximately 50 MeV. Composites of
and
states bound by pion exchange alone are expected near the thresholds, while in the light meson sector one generally needs some additional short range attraction to form bound states. The quantum numbers of these states areI=0, andJ
PC=0–+, 1++ for the
states andI=0,J
PC=0++, O–+, 1+– and 2++ for the
composites. In
the states:
b
(10545),
b1(10562) are predicted and in
, one finds the states:
b
(10590),
bQ
(10582),h
b(10608),
b2(10602). Near the
threshold the states:
c
(3870),
c0(3870) are predicted, and near the
threshold one finds the states:
b0(4015),
c
(4015),h
c(4015),
c2(4015). Within the light meson sector pion exchange gives strong attraction for
and
systems with quantum numbers where the best non-
candidates exist, although pion exchange alone is not strong enough to support such bound states. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the (1440) and thef
1 (1420) are mainly
composites and thef
0(1710) mainly a
bound state, while thef
0(1515) andf
2(1520) could be predominantly
composites. If the predicted
and
states are found, these would support this interpretation of the light states. In channels with exotic flavour orCP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, althoughB*B* may be an exception. 相似文献
5.
We give a realization of the quantum affine Lie algebras
and
in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter q being related to the statistical parameter of the anyons by q = ei. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel [1] fermionic construction of undeformed affine Lie algebras. 相似文献
6.
In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form
is studied from the point of view of *-automorphisms of the CCRC*-algebra
(see Ref. [1, 2]). It is proved that those Hamiltonians do not induce *-automorphisms of this algebra in the cases: a)
and b)V L
(,dx) L
1 (,dx), except when the potential is trivial. 相似文献
7.
T. Kawai 《Foundations of Physics》1975,5(1):143-158
Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL
c(
, x)=(M/2)gij(x)
i
j–v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. 相似文献
8.
Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal groupSO
e
(5,1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (-sheeted) covering group* of the Minkowskian conformal group SO
e
(4, 2)2. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an -sheeted covering
of Minkowski-spaceM
4. It is known that* can act on this space
and that
admits a globally*-invariant causal ordering;
is thus the natural space on which a globally*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal HamiltonianH=1/2(P
0+K
0).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup
of to unitary representations of*. 相似文献
9.
The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on
d
, d2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the Ising spins are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to . We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed. 相似文献
10.
We consider cosmology in the framework of a material reference system of
particles, including the effects of quantum recoil induced by closed-string probe particles. We find a time-dependent contribution to the cosmological vacuum energy, which relaxes to zero as 1/t
2 for large times t. If this energy density is dominant, the Universe expands with a scale factor R(t)t
2. We show that this possibility is compatible with recent observational constraints from high–redshift supernovae, and may also respect other phenomenological bounds on time variation in the vacuum energy imposed by early cosmology. 相似文献
11.
We consider the crystal structure of the level zero extremal weight modules V() using the crystal base of the quantum affine algebra constructed in Duke Math. J.
99 (1999), 455–487. This approach yields an explicit form for extremal weight vectors in the U
– part of each connected component of the crystal, which are given as Schur functions in the imaginary root vectors. We show the map
induces a correspondence between the global crystal base of V() and elements
. 相似文献
12.
A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy K. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator
acting on a distribution in phase space, it is shown that i[L,
]KI (I=identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a finite duration of presence. Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator. 相似文献
13.
Marc A. Rieffel 《Communications in Mathematical Physics》1995,171(1):181-201
LetG be a Lie group. For any Abelian subalgebra
of the Lie algebra g ofG, and any
, the difference of the left and right translates ofr gives a compatible Poisson bracket onG. We show how to construct the corresponding quantum group, in theC
*-algebra setting. The main tool used is the general deformation quantization construction developed earlier by the author for actions of vector groups onC
*-algebras.The research reported on here was supported in part by National Science Foundation grant DMS-9303386. 相似文献
14.
Decio Cocolicchio 《Foundations of Physics Letters》1990,3(4):359-365
A bound on theK
oscillating parameter has been obtained by some models of nonlocality. In this paper we stress the fact that aø factory to test the CP-violating parameters in theK system can also probe, through correlated observations of two
0, the incompatibility between the quantum mechanics and these formulations of the local realism. 相似文献
15.
We classify all the quasifinite highest-weight modules over the central extension of the Lie algebra of matrix quantum pseudo-differential operators, and obtain them in terms of representation theory of the Lie algebra
(, R
m
) of infinite matrices with only finitely many nonzero diagonals over the algebra R
m
=
[t]/(t
m+1). We also classify the unitary ones. 相似文献
16.
Kh. Namsrai 《International Journal of Theoretical Physics》1987,26(3):247-273
Introducing quantum space-time into physics by means of the transformation language of noncommuting coordinates gives a simple scheme of generalizing the tensor analysis. The general covariance principle for the quantum space-time case is discussed, within which one can obtain the covariant structure of basic tensor quantities and the motion equation for a particle in a gravitational field. Definitions of covariant derivatives and curvature are also generalized in the given case. It turns out that the covariant structure of the Riemann-Christoffel curvature tensor is not preserved in quantum space-time. However, if the curvature tensor
v
(z) is redetermined up to the value of theL
2 term, then its covariant structure is achieved, and it, in turn, allows us to reconstruct the Einstein equation in quantum space-time. 相似文献
17.
V. G. Knizhnik 《Communications in Mathematical Physics》1987,112(4):567-590
The properties of analytic fields on a Riemann surface represented by a branch covering of 1 are investigated in detail. Branch points are shown to correspond to the vertex operators with simple conformal properties. As applications we compute determinants of
operators forZ
n
-symmetric surfaces and obtain various representations for the two-loop measure in the bosonic string theory together with various identities for theta-functions of hyperelliptic surfaces. We also present an integral representation for the quantum part of the twist field correlation functions, which describe propagation of the string on the orbifold background. We also calculate the quantum part of the structure constants of the twist-field operator algebra, generalizing the results of Dixon, Friedan, Martinec, and Shenker. 相似文献
18.
There is an intriguing discrepancy between
values measured directly at the CERNZ
0-factory and low-energy (at few GeV) measurements transformed toQ=M
z0 by a massless QCD
evolution relation. There exists and attempt to reconcile this discrepancy by introducing a light gluinog in the MSSM. We study in detail the influence of heavy thresholds on
evolution. First, we construct the exact explicit solution to the mass-dependent two-loop RG equation for the running
. This solution describes heavy thresholds smoothly. Second, we use this solution to recalculate a new
values corresponding to low-energy input data. Our analysis demonstrates that usingmass-dependent RG procedure generally produces corrections of two types: Asymptotic correction due to effective shift of threshold position; Local threshold correction only for the case when input experiment lies in the close vicinity of heavy particle threshold:Q
expt
-M
h
. Both effects result in the effective shift of the
values of the order of 10–3. However, the second one could be enhanced when the gluino mass is close to a heavy quark mass. For such a case the sum effect could be important for the discussion of the light gluino existence as it further changes theg mass.Work supported in part by INTAS-93-1180 相似文献
19.
We construct a non-commutative *-algebra
which is a quantum deformation of the algebra of continuous functions on the closed unit disc
.
is generated by the Toeplitz operators on a suitable Hilbert space of holomorphic functions onU.Supported in part by the National Science Foundation under grant DMS/PHY 88-16214 相似文献
20.
Dabin Lin Zhenrong Li Shujun Zhang Zhuo Xu Xi Yao 《Solid State Communications》2009,149(39-40):1646-1649
(K0.5Na0.5)NbO3 (KNN) single crystals were grown using a high temperature flux method. The dielectric permittivity was measured as a function of temperature for [001]-oriented KNN single crystals. The ferroelectric phase transition temperatures, including the rhombohedral–orthorhombic TR−O, orthorhombic–tetragonal TO−T and tetragonal–cubic TC were found to be located at −149 C, 205 C and 393 C, respectively. The domain structure evolution with an increasing temperature in [001]-oriented KNN single crystal was observed using polarized light microscopy (PLM), where three distinguished changes of the domain structures were found to occur at −150 C, 213 C and 400 C, corresponding to the three phase transition temperatures. 相似文献