Collection Of Spins Research Articles

Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems

We consider the problem of determining the energy distribution of quantum states that satisfy exponential decay of correlation and product states, with respect to a quantum local Hamiltonian on a spin lattice. For a quantum state on a D-dimensional lattice that has correlation length σ and has average energy e with respect to a given local Hamiltonian (with n local terms, each of which has norm at most 1), we show that the overlap of this state with eigenspace of energy f is at most . This bound holds whenever . Thus, on a one-dimensional lattice, the tail of the energy distribution decays exponentially with the energy. For product states, we improve above result to obtain a Gaussian decay in energy, even for quantum spin systems without an underlying lattice structure. Given a product state on a collection of spins which has average energy e with respect to a local Hamiltonian (with n local terms and each local term overlapping with at most m other local terms), we show that the overlap of this state with eigenspace of energy f is at most . This bound holds whenever .

The role of disorder in the dynamics of critical fluctuations of mean field models

The purpose of this paper is to analyze how disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environ- ment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result con- cerns the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).

Passage-time distributions from a spin-boson detector model

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like ${E}^{\ensuremath{-}3∕4}$, which improves previous ${E}^{\ensuremath{-}1}$ estimates, obtained with a quantum clock model.

Investigation of a quantum mechanical detector model for moving, spread-out particles

We investigate a fully quantum mechanical spin model for the detection of a moving particle. This model, developed in earlier work, is based on a collection of spins at fixed locations and in a metastable state, with the particle locally enhancing the coupling of the spins to an environment of bosons. Appearance of bosons from particular spins signals the presence of the particle at the spin location, and the first boson indicates its arrival. The original model used discrete boson modes. Here we treat the continuum limit, under the assumption of the Markov property, and calculate the arrival-time distribution for a particle to reach a specific region.

Coherent control of spin squeezing

We report an interaction that controls spin squeezing in a collection of spin 1/2 particles. We describe how spin squeezing can be generated and maintained in time. Our scheme can be applied to control the spin squeezing in a Bose condensate with two internal spin states.

Multidimensional k-space model for analysis of flow-related phenomena in MR imaging

The multidimensional partition model, which combines the k-space description of magnetic resonance imaging pulse sequences with a partition concept, has been developed to model flow-related effects. A partition represents the magnetization created due to excitation by a given radiofrequency pulse. In the present model, it is visualized as a set of parameters rather than a vector sum taken over a collection of spins. The phase dispersion due to velocity and higher orders of motion is described by adding new dimensions to the three spatial k-space dimensions. The computer implementation of the model is capable of simulating the outcome from pulse sequences used in clinical routines and it does not need assumptions regarding pulse sequence parameters. Furthermore, flow-induced effects due to phase dispersion, caused by movements in a magnetic field gradient, as well as the inflow of unsaturated spins, are handled by the model. Constant or varying (pulsatile) flow velocity may be assigned together with different velocity profiles (e.g., plug flow, laminar flow) over a simulated vessel. The model makes it possible to simulate images of an object containing vessels with pulsatile laminar flow pattern, scanned using a three-dimensional angiography pulse sequence, in <10 min on a Pentium-based PC system. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 115–127, 1999

A multidimensional partition analysis of SSFP image pulse sequences.

The k-space description, of MRI pulse sequences, has been combined with a partition model in order to model the image reconstruction and the contrast behaviour found in SSFP pulse sequences. A partition represents the magnetisation created, due to excitation by a given rf pulse. In the present model, it is visualised as a set of parameters rather than a vector sum taken over a collection of spins. A multidimensional parameter space, where each dimension is associated with one of the partition parameters, is introduced in order to describe the interaction between partitions and pulse sequence events (e.g., rf pulses and gradients). The three k-space dimensions form the first three dimensions and higher orders are used to handle phase dispersions due to diffusion and main field inhomogeneities. The model makes it possible to perform fast simulation of images resulting from general SSFP pulse sequences. A computer implementation generates images (256 matrix), containing more than 10 different T1/T2 combinations, in less than 45 s on a 120 MHz Pentium computer. The contrast behaviour and signal intensities found in simulated images show excellent agreement with data generated using a clinical MRI scanner system.