Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(1)(F)) and antiferromagnetic (J(1)(A)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(2)(F)). In this model frustration is present due to the non-zero J(2)(F). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(2)(F) and large J(1)(F)/J(1)(A). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(1)(F), the phase diagram in the space of J(1)(A)-J(2)(F) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

Revisiting neutrino masses from Planck scale operators

Planck scale lepton number violation is an interesting and natural possibility to explain nonzero neutrino masses. We consider such operators in the context of Randall-Sundrum (RS1) scenarios. Implementation of this scenario with a single Higgs localized on the IR brane (standard RS1) is not phenomenologically viable as they lead to inconsistencies in the charged lepton mass fits. In this paper we propose a setup with two Higgs doublets. We present a detailed numerical analysis of the fits to fermion masses and mixing angles. This model solves the issues regarding the fermion mass fits but solutions with consistent electroweak symmetry breaking are highly fine-tuned. A simple resolution is to consider supersymmetry in the bulk and a detailed discussion of which is provided. Constraints from flavor are found to be strong and minimal flavor violation (MFV) is imposed to alleviate them.

Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

Generalizations and extensions of the Fokker-Planck-Kolmogorov equations

The problem of determining probability density functions of general transformations of random processes is considered in this thesis. A method of solution is developed in which partial differential equations satisfied by the unknown density function are derived. These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and are shown to imply the classical equations for certain classes of Markov processes. Extensions of the generalized equations which overcome degeneracy occurring in the steady-state case are also obtained.

The equations of Darling and Siegert are derived as special cases of the generalized equations thereby providing unity to two previously existing theories. A technique for treating non-Markov processes by studying closely related Markov processes is proposed and is seen to yield the Darling and Siegert equations directly from the classical Fokker-Planck-Kolmogorov equations.

As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter. These equations are solved for the density of the output of an arbitrary linear filter excited by Markov Gaussian noise and for the density of the output of an RC filter excited by the Poisson square wave. This latter density is also found by using the extensions of the generalized equations mentioned above. Finally, some new approaches for finding the output probability density function of an RC filter-limiter-RC filter system driven by white Gaussian noise are included. The results in this case exhibit the data required for complete solution and clearly illustrate some of the mathematical difficulties inherent to the use of the generalized equations.

Spin squeezing, macrorealism and the heisenberg uncertainty principle

169 p.

A interpretação filosófica da mecânica quântica de Werner Heisenberg: ontologia matemática e a crise nos fundamentos da lógica clássica

Qual a Filosofia da Natureza que podemos inferir da Física Contemporânea? Para Werner Karl Heisenberg, prêmio Nobel de Física de 1932, a ontologia da Ciência Moderna, estruturada no materialismo, no mecanicismo e no determinismo já não pode servir de fundamento para a nova Física. Esta requer uma nova base ontológica, onde o antirrealismo, seguido de um formalismo puro, aparece como o princípio basilar de uma nova Filosofia Natural. Este trabalho visa investigar o pensamento filosófico, a ontologia antirrealista, formalista, a abordagem da tradição filosófica e da história da ciência de Werner Heisenberg e sua contribuição para a interpretação da mecânica quântica.

Como o homem se orienta no mundo? Uma discussão com Werner Heisenberg

Entre os anos de 1942 e 1943, Werner Heisenberg produziu um manuscrito que resguarda as suas mais graves e amplas concepções filosóficas. Intitulado pelos editores como Ordenação da Realidade após a morte do autor, o escrito diagnostica uma profunda crise não somente na esfera da ciência, mas igualmente nos campos da moral e da política. O propósito desta tese é discutir as ideias apresentadas por Heisenberg, a partir da questão que compartilhamos com o físico sobre como o homem se orienta no mundo. A crise serve para demonstrar a necessidade de rearticulação da ontologia. Não se trata simplesmente de reconsiderar a divisão clássica entre objetividade e subjetividade, entre lei moral e sentimento, entre fundar a política na igualdade ou na liberdade. Tais dicotomias devem ser suspensas em prol de uma reconsideração sobre a determinação do ente a partir da totalidade de mundo, os processos de temporalização que conferem a medida das atividades humanas e as diferentes fontes que oferecem ao homem o poder de estabelecer comunidade. Reformular o conceito de realidade, bem como estabelecer a sua possibilidade de compreensão a partir de níveis e âmbitos, tal é o caminho da nossa confrontação com Heisenberg, a qual supera a trivialidade de um realismo como suposição de coisas simplesmente dadas.

DTADH and quantum critical phenomena caused by anisotropy and external magnetic field for spin-1/2 Heisenberg diamond chains

Using the transfer matrix renormalization group (TMRG) method, we study the connection between the first derivative of the thermal average of driving-term Hamiltonian (DTADH) and the trace of quantum critical behaviors at finite temperatures. Connecting with the exact diagonalization method, we give the phase diagrams and analyze the properties of each phase for both the ferromagnetic and anti-ferromagnetic frustrated J(3) anisotropy diamond chain models. The finite-temperature scaling behaviors near the critical regions are also investigated. Further, we show the critical behaviors driven by external magnetic field, analyze the formation of the 1/3 magnetic plateau and the influence of different interactions on those critical points for both the ferrimagnetic and anti-ferromagnetic distorted diamond chains.

Quantum teleportation via a two-qubit Heisenberg XXZ chain - effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ, chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Thermodynamic properties of Cu-3(CO3)(2)(OH)(2) and the spin-1/2 distorted diamond Heisenberg chain

The thermodynamic properties of the spin-1/2 diamond quantum Heisenberg chain model have been investigated by means of the transfer matrix renormalization group (TMRG) method. Considering different crystal structures, by changing the interactions among different spins and the external magnetic fields, we first investigate the magnetic susceptibility, magnetization, and specific heat of the distorted diamond chain as a model of ferrimagnetic spin systems. The susceptibility and the specific heat show different features for different ferromagnetic (F) and antiferromagnetic (AF) interactions and different magnetic fields. A 1/3 magnetization plateau is observed at low temperature in a magnetization curve. Then, we discuss the theoretical mechanism of the double-peak structure of the magnetic susceptibility and the three-peak structure of the specific heat of the compound Cu-3(CO3)(2)(OH)(2), on which an elegant measurement was performed by Kikuchi [Phys. Rev. Lett. 94, 227201 (2005)]. Our computed results are consistent with the main characteristics of the experimental data. Meanwhile, we find that the double-peak structure of susceptibility can be found in several different kinds of spin interactions in the diamond chain. Moreover, a three-peak behavior is observed in the TMRG results of magnetic susceptibility. In addition, we perform calculations relevant for some experiments and explain the characteristics of these materials. (c) 2007 American Institute of Physics.

Optimal teleportation via thermal entangled states of a two-qubit Heisenberg chain

We study the optimal teleportation based on Bell measurements via the thermal states of a two-qubit Heisenberg XXX chain in the presence of the Dzyaloshinsky-Moriya (DM) anisotropic antisymmetric interaction and obtain an optimal unitary transformation. The explicit expressions of the output state and the teleportation fidelity are presented and compared with those of the standard protocol. It is shown that in this protocol the teleportation fidelity is always larger and the unit fidelity is achieved at zero temperature. The DM interaction can enhance the teleportation fidelity at finite temperatures, as opposed to the effect of the interaction in the standard protocol. Cases with other types of anisotropies are also discussed. Copyright (C) EPLA, 2009

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

The thermal entanglement in a two-qubit Heisenberg XXZ spin chain is investigated under an inhomogeneous magnetic field b. We show that the ground-state entanglement is independent of the interaction of z-component J(z). The thermal entanglement at the fixed temperature can be enhanced when J(z) increases. We strictly show that for any temperature T and J(z), the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field b(c) is independent of J(z). The critical magnetic field B-c increases with the increasing parallel to b parallel to but the maximum entanglement value that the system can arrive at becomes smaller.

Interplay between the Dzyaloshinskii-Moriya anisotropic antisymmetric interaction and the SWAP operation in a two-qubit Heisenberg model

The SWAP operation in a two-qubit Heisenberg model in the presence of Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction is investigated. 1t is shown that the SWAP operation can be implemented for some kinds of DM coupling and the influence of DM couplings is divided into different cases. The conditions of the DM coupling under which the SWAP operation is feasible are established. (C) 2007 Elsevier B.V. All rights reserved.

SWAP operation in the two-qubit Heisenberg XXZ model: Effects of anisotropy and magnetic field

In this paper we study the SWAP operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter lambda within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.