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1.
Point interactions for pseudo-differential operators are studied. Necessary and sufficient conditions for a pseudo-differential operator to have nontrivial point perturbations are given. The results are applied to the construction of relativistic spin zero Hamiltonians with point interactions. 相似文献
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An effective algorithm is provided for determining the number of negative eigenvalues of a one-dimensional Schrödinger operator with point interactions in terms of the intensities and the distances between the interactions. 相似文献
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We consider the problem of constraining a particle to a smooth compact submanifold Σ of configuration space using a sequence
of increasing potentials. We compare the classical and quantum versions of this procedure. This leads to new results in both
cases: an unbounded energy theorem in the classical case, and a quantum averaging theorem. Our two step approach, consisting
of an expansion in a dilation parameter, followed by averaging in normal directions, emphasizes the role of the normal bundle
of Σ, and shows when the limiting phase space will be larger (or different) than expected.
Received: 16 November 2000 / Accepted: 2 February 2001 相似文献
6.
We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal
equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the
reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three
asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes
continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ2τ → 0 and the critical case λ2τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a
non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative
regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction
Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model
whose asymptotic effective evolution is generated by this Lindblad operator. 相似文献
7.
We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr?dinger operators which is based
on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result
to various models, including the Fibonacci Hamiltonian.
Received: 5 June 2002 / Accepted: 20 January 2003
Published online: 28 March 2003
RID="⋆"
ID="⋆" D.D. was supported in part by NSF Grant No. DMS–0227289
Communicated by M. Aizenman 相似文献
8.
We theoretically study the spin properties of two interacting electrons confined in the IhAs parallel coupled quantum dots (CQDs) with spin-orbit interactions (SOI) by exact diagonalization method. Through the SOI induced spin mixing of the singlet and the triplet states, we show the different spin properties for the weak and strong SOI. We investigate the coherent singlet-triplet spin oscillations of the two electrons under the SOI, and demonstrate the detailed behaviors of the spin oscillations depending on the SOI strengths, the inter-dot separations and the external magnetic fields. To better understand the underlying physics of the spin dynamics, we introduce a four-level model Hamiltonian for both weak and strong SOI, and find that the SOI induced in plane effective magnetic fields can be quantitatively extracted from the two-electron excitation energy spectra. 相似文献
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James F. Woodward 《Foundations of Physics》2001,31(5):819-835
Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electrically charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reaction forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. 相似文献
11.
N = 4 superconformal quantum mechanics of nonrelativistic particles in the typical 1/x2-potentials, which holds not only supersymmetry but also dynamical conformal symmetry, is studied. The corresponding superconformal quantum mechanical algebra, which contains supersymmetric quantum mechanical algebra with four supercharges and conformal algebra as subalgebras, and its two canonical group chains are established. 相似文献
12.
We investigate the leading low-energy falloff of the integrated density of states of a charged quantum particle in the Euclidean plane subject to a perpendicular constant magnetic field and repulsive impurities randomly distributed according to Poisson's law. This so-called magnetic Lifshits tail was determined by K. Broderix et al. [J. Stat. Phys.
80:1 (1995)] for algebraically decaying and by L. Erds [Probab. Theory Relat. Fields
112:321 (1998)] for compactly supported single-impurity potentials. While the result in the first case coincides with the corresponding classical one, the Lifshits tail in Erds' case exhibits a genuine quantum behavior. Building on both works, we determine magnetic Lifshits tails for a wide class of positive impurity potentials with a leading long-distance decay in between these limiting cases. Gaussian decay may be shown to discriminate between classical and quantum behavior. The Lifshits tail caused by Gaussian decay reveals power-law falloff with an exponent not yet completely determined. 相似文献
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Diego L. Rapoport 《Foundations of Physics》2007,37(4-5):813-854
We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries,
and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion
one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend
this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW
geometry in state-space associated with the gradient of the quantum-mechanical expectation value of a self-adjoint operator
given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms
of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian
motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases.
We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an
active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of
the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev. 相似文献
15.
Quantum gates are described by unitary operators. We discuss the construction of Hamilton operators from the unitary operators. Different techniques are applied. 相似文献
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Extending the work of Lewis and Leach on classical invariants for solving the classical equation of motion in one-dimensional system, the quantum invariants in polynomial form of momentum are obtained. The involved Hamiltonian is time-dependent and quadratic in momentum. 相似文献
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Through the Jordan-Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called ``spin waves', which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings. 相似文献
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A new approach to the inverse scattering problem proposed by Schroer, is applied to two-dimensional integrable quantum field theories. For any two-particle S-matrix S
2 which is analytic in the physical sheet, quantum fields are constructed which are localizable in wedge-shaped regions of Minkowski space and whose two-particle scattering is described by the given S
2. These fields are polarization-free in the sense that they create one-particle states from the vacuum without polarization clouds. Thus they provide examples of temperate polarization-free generators in the presence of nontrivial interaction. 相似文献
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We consider three Ginibre ensembles (real, complex and quaternion-real) with deformed measures and relate them to known integrable systems by presenting partition functions of these ensembles in form of fermionic expectation values. We also introduce double deformed Dyson–Wigner ensembles and compare their fermionic representations with those of Ginibre ensembles. 相似文献