1207 research outputs found
Sort by
Perfect Transfer of Arbitrary States in Quantum Spin Networks
Get PDFWe propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2*log_3(N) is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done in [1]
Large deviations for trapped interacting Brownian particles and paths
Get PDFWe introduce two probabilistic models for N interacting Brownian motions moving in a trap in R d under mutually repellent forces. The two models are defined in terms of transformed path measures on finite time intervals under a trap Hamiltonian and two respective pair-interaction Hamiltonians. The first pair interaction exhibits a particle repellency, while the second one imposes a path repellency. We analyse both models in the limit of diverging time with fixed number N of Brownian motions. In particular, we prove large deviations principles for the normalised occupation measures. The minimisers of the rate functions are related to a certain associated operator, the Hamilton operator for a system of N interacting trapped particles. More precisely, in the particle-repellency model, the minimiser is its ground state, and in the path-repellency model, the minimisers are its ground product-states. In the case of path-repellency, we also discuss the case of a Dirac-type interaction, which is rigorously defined in terms of Brownian intersection local times. We prove a large-deviation result for a discrete variant of the model. This study is a contribution to the search for a mathematical formulation of the quantum system of N trapped interacting bosons as a model for Bose-Einstein condensation, motivated by the success of the famous 1995 experiments. Recently, Lieb et al. described the large-N behaviour of the ground state in terms of the well-known Gross-Pitaevskii formula, involving the scattering length of the pair potential. We prove that the large-N behaviour of the ground product-states is also described by the Gross-Pitaevskii formula, however with the scattering length of the pair potential replaced by its integral
Quantization of Neveu-Schwarz-Ramond Superstring Model in 10+2-dimensional Spacetime
Get PDFWe construct a Neveu-Schwarz-Ramond superstring model which is invariant under supersymmetric U(1)_V × U(1)_A gauge transformations as well as the super-general coordinate, the super local Lorentz and the super-Weyl transformations on the string world-sheet. We quantize the superstring model by covariant BRST formulation á la Batalin and Vilkowsky and noncovariant light-cone gauge formulation. Upon the quantizations the model turns out to be formulated consistently in 10+2-dimensional background spacetime involving two time dimensions
Fuzzy Complex Quadrics and Spheres
Get PDFA matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannian of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for describing truncations of harmonic expansions of functions on N-spheres. An Inönü-Wigner contraction of the quadric gives the co-tangent bundle to the commutative sphere in the continuum limit. It is shown how the degrees of freedom for the sphere can be projected out of a finite dimensional functional integral, using second-order Casimirs, giving a well-defined procedure for construction functional integrals over fuzzy spheres of any dimension
A new theory of superfluidity
Get PDFThe understanding of superfluidity represents one of the most challenging problems in modern physics. From the observations of [1-3], in various respects the Bogoliubov theory [4—8] is not appropriate as the model of superfluidity for Helium 4. His outstanding achievement, i.e., the derivation of the Landau-type excitation spectrum [9, 10] from the full interacting Hamiltonian, is based on a series of recipes or approximations, which were shown to be wrong, even from their starting point [11—14]. We therefore present some very promising new results performed in [15]. In particular, we explain a new theory of superfluidity at all temperatures. At this point we then touch one of the most fascinating problems of contemporary mathematical physics the proof of the existence of superfluidity in interacting (non-dilute) systems
Calculation of the Invariant Measures at Weak Disorder for the Two-Line Anderson Model
Get PDFWe compute the invariant measures in the weak disorder limit, for the Anderson model on two coupled chains. These measures live on a three-dimensional projective space, and we use a total set of functions on this space to characterise the measures. It turns out that at zero energy, there is a similar anomaly as first found by Kappus and Wegner for the single chain, but that, in addition, the measures take a different form on different regions of the spectrum
The spectrum of the Dirac operator on coset spaces with homogeneous Gauge fields
Get PDFThe spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is derived from the spin-connection. It is shown how the degeneracy of the lowest Landau level in the recently proposed higher dimensional quantum Hall effect is related to the Atiyah-Singer index theorem for the Dirac operator on a compact coset space
A Fuzzy Three Sphere and Fuzzy Tori
Get PDFA fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves only states corresponding to fuzzy spheres in the low energy spectrum. The construction of a fuzzy circle opens the way to fuzzy tori of any dimension, thus circumventing the problem of power law corrections in possible numerical simulations on these spaces