Search results for "Mathematical physics"
showing 10 items of 2687 documents
Many-qubit quantum state transfer via spin chains
2015
The transfer of an unknown quantum state, from a sender to a receiver, is one of the main requirements to perform quantum information processing tasks. In this respect, the state transfer of a single qubit by means of spin chains has been widely discussed, and many protocols aiming at performing this task have been proposed. Nevertheless, the state transfer of more than one qubit has not been properly addressed so far. In this paper, we present a modified version of a recently proposed quantum state transfer protocol [Phys. Rev. A 87, 062309 (2013)] to obtain a quantum channel for the transfer of two qubits. This goal is achieved by exploiting Rabi-like oscillations due to excitations induc…
Generalized Bloch spheres form-qubit states
2006
m-Qubit states are imbedded in $\mathfrak{Cl}_{2^m}$ Clifford algebras. Their probability spectra then depend on $O(2m)$ or $O(2m+1)$ invariants. Parameter domains for $O(2m(+1))-$ vector and tensor configurations, generalizing the notion of a Bloch sphere, are derived.
N-qubit states as points on the Bloch sphere
2009
We show how the Majorana representation can be used to express the pure states of an N-qubit system as points on the Bloch sphere. We compare this geometrical representation of N-qubit states with an alternative one, proposed recently by the present authors.
Exactly solvable time-dependent pseudo-Hermitian su(1,1) Hamiltonian models
2018
An exact analytical treatment of the dynamical problem for time-dependent 2x2 pseudo-hermitian su(1,1) Hamiltonians is reported. A class of exactly solvable and physically transparent new scenarios are identified within both classical and quantum contexts. Such a class is spanned by a positive parameter $\nu$ that allows to distinguish two different dynamical regimes. Our results are usefully employed for exactly solving a classical propagation problem in a guided wave optics scenario. The usefulness of our procedure in a quantum context is illustrated by defining and investigating the su(1,1) "Rabi" scenario bringing to light analogies and differences with the standard su(2) Rabi model. Ou…
Density-potential mappings in quantum dynamics
2012
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an ex…
The Kadanoff–Baym approach to double excitations in finite systems
2011
We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are cha…
Macroscopic conductivity of free fermions in disordered media
2014
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint. We show, in particular, the existence and finiteness of the conductivity measure $\mu _{\mathbf{\Sigma }}$ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, $\mu _{\mathbf{\Sigma }}$ converges in the weak$^{\ast } $-topology to the trivial measure in the case of perfect insulators (strong disorder, compl…
Quantum tomography and nonlocality
2015
We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.
Dynamical Casimir-Polder potentials in non-adiabatic conditions
2014
In this paper we review different aspects of the dynamical Casimir¿Polder potential between a neutral atom and a perfectly conducting plate under nonequilibrium conditions. In order to calculate the time evolution of the atom¿wall Casimir¿Polder potential, we solve the Heisenberg equations describing the dynamics of the coupled system using an iterative technique. Different nonequilibrium initial states are considered, such as bare and partially dressed states. The partially dressed states considered are obtained by a sudden change of a physical parameter of the atom or of its position relative to the conducting plate. Experimental feasibility of detecting the considered dynamical effects i…
Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions
2006
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of \alpha_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a…