Search results for "Hamiltonian"
showing 10 items of 662 documents
Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
2022
In some recent literature the role of non self-adjoint Hamiltonians, $H\neq H^\dagger$, is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schr\"odinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected to the standard Heisenberg picture for systems driven by self-adjoint Hamiltonians. In particular, the role of the symmetries, *-derivations and integrals of motion is discussed.
Reconstruction of Hamiltonians from given time evolutions
2010
In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state of the system. Our approach exploits the equivalence between an action of the group of evolution operators over the state space and an adjoint action of the unitary group over Hermitian matrices. The method is illustrated by two examples involving a pure and a mixed state.
Quantum correlations in dissipative gain–loss systems across exceptional points
2023
We investigate the behavior of correlations dynamics in a dissipative gain-loss system. First, we consider a setup made of two coupled lossy oscillators, with one of them subject to a local gain. This provides a more realistic platform to implement parity-time (PT) symmetry circumventing the implementation of a pure gain. We show how the qualitative dynamics of correlations resembles that for a pure-gain-loss setup. The major quantitative effect is that quantum correlations are reduced, while total ones are enhanced. Second, we study the behavior of these correlations across an exceptional point (EP) outside of the PT-symmetric regime of parameters, observing how different behaviors across …
Bottomonium spectroscopy and radiative transitions involving theχbJ(1P,2P)states atBaBar
2014
We use (121±1) million Υ(3S) and (98±1) million Υ(2S) mesons recorded by the BABAR detector at the PEP-II e^+e^− collider at SLAC to perform a study of radiative transitions involving the χ_(bJ)(1P,2P) states in exclusive decays with μ^+μ^−γγ final states. We reconstruct twelve channels in four cascades using two complementary methods. In the first we identify both signal photon candidates in the electromagnetic calorimeter (EMC), employ a calorimeter timing-based technique to reduce backgrounds, and determine branching-ratio products and fine mass splittings. These results include the best observational significance yet for the χ_(b0)(2P)→γΥ(2S) and χ_(b0)(1P)→γΥ(1S) transitions. In the se…
Including long-distance effects in theKL−KSmass splitting
1990
In the framework of the standard model we propose an approach to the computation of the {ital K}{sub {ital L}}-{ital K}{sub {ital S}} mass difference which does not rely on an effective local Hamiltonian. Using partial conservation of axial-vector current, low-momentum Ward identities, and working at leading order in 1/{ital N}{sub {ital c}}, we relate box diagrams to others where strong interactions can be resummed. After subtracting the {ital K}-to-vacuum transitions, an expression involving only hadronic quantities is obtained. A numerical evaluation is performed by using a method of analytic continuation from the high-energy behavior given by QCD. The resulting contribution is found sma…
B0−B¯0Mixing beyond Factorization in QCD Sum Rules
2003
We present a calculation of the B°-B° mixing matrix element in the framework of QCD sum rules for three-point functions. We compute α s corrections to a three-point function at the three-loop level in QCD perturbation theory, which allows one to extract the matrix element with next-to-leading order (NLO) accuracy. This calculation is imperative for a consistent evaluation of experimentally measured mixing parameters since the coefficient functions of the effective Hamiltonian for B 0 -B 0 mixing are known at NLO. We find that radiative corrections violate factorization at NLO; this violation is under full control and amounts to 10%. The resulting value of the B parameter is found to be B B …
Spectrum of SU(2) gauge theory with two fermions in the adjoint representation
2008
We present preliminary results of lattice simulations of SU(2) gauge theory with two Wilson fermions in the adjoint representation. This theory has recently attracted considerable attention because it might possess an infrared fixed point (or an almost-fixed-point), and hence be a candidate for a walking technicolor theory. In this work we study the particle spectrum of the theory, and compare it with more familiar spectrum of the theory with SU(2) gauge fields and two flavors of fundamental representation fermions.
Off-forward Matrix Elements in Light-front Hamiltonian QCD
2002
We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.
Exact Solution of Quantum Optical Models by Algebraic Bethe Ansatz Methods
1996
From long standing interests in solitons and integrable systems, e.g. SIT (1968– 74)1,2, “optical solitons” CQ04 (1977)3, we solve exactly, by algebraic Bettie ansatz (= quantum inverse) methods4, models of importance to quantum optics including the quantum Maxwell-Bloch envelope equations for plane-wave quantum self-induced transparency (SIT) in one space variable (x) and one time (t)2; and in the one tinte (t)5 a family of models surrounding and extending the Tavis-Cummings model6 of N 2-level atoms coupled to one cavity mode for ideal cavity (Q = ∞) QED. Additional Kerr type nonlinearities or Stark shifted levels can he incorporated into the Hamiltonian H of one of the most general model…
Geometry of quantum phase transitions
2020
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas i…