Error Avoiding Quantum Codes

The existence is proved of a class of open quantum systems that admits a linear subspace ${\cal C}$ of the space of states such that the restriction of the dynamical semigroup to the states built over $\cal C$ is unitary. Such subspace allows for error-avoiding (noiseless) enconding of quantum information.Comment: 9 pages, LaTe

Where do bosons actually belong?

We explore a variety of reasons for considering su(1,1) instead of the customary h(1) as the natural unifying frame for characterizing boson systems. Resorting to the Lie-Hopf structure of these algebras, that shows how the Bose-Einstein statistics for identical bosons is correctly given in the su(1,1) framework, we prove that quantization of Maxwell's equations leads to su(1,1), relativistic covariance being naturally recognized as an internal symmetry of this dynamical algebra. Moreover su(1,1) rather than h(1) coordinates are associated to circularly polarized electromagnetic waves. As for interacting bosons, the su(1,1) formulation of the Jaynes-Cummings model is discussed, showing its advantages over h(1).Comment: 9 pages, to appear in J. Phys. A: Math. Theo

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz

Quantum symmetries induced by phonons in the Hubbard model

We show how the addition of a phonon field to the Hubbard model deforms the superconducting su(2) part of the global symmetry Lie algebra su(2)⊗su(2)/openZ2, holding at half filling for the customary model, into a quantum [su(2)]q symmetry, holding for a filling which depends on the electron-phonon interaction strength. Such symmetry originates in the feature that in the presence of phonons the hopping amplitude turns out to depend on the coupling strength. The states generated by resorting to this q symmetry exhibit both off-diagonal long-range order and pairing

The Topological Field Theory of Data: a program towards a novel strategy for data mining through data language

This paper aims to challenge the current thinking in IT for the 'Big Data' question, proposing - almost verbatim, with no formulas - a program aiming to construct an innovative methodology to perform data analytics in a way that returns an automaton as a recognizer of the data language: a Field Theory of Data. We suggest to build, directly out of probing data space, a theoretical framework enabling us to extract the manifold hidden relations (patterns) that exist among data, as correlations depending on the semantics generated by the mining context. The program, that is grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a Topological Field Theory of Data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns

New quantumness domains through generalized squeezed states

Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its Schwinger two-photon realization are proposed as squeezed states. The physical implication of this assumption is that two additional degrees of freedom become available for the control of quantum optical systems. The resulting physical predictions are evaluated in terms of quadrature squeezing and photon statistics, while the application to a Mach–Zehnder interferometer is discussed to show the emergence of nonclassical regions, characterized by negative values of Mandel’s parameter, which cannot be anticipated by the current formulation, and then outline future possible use in quantum technologies

Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model

We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1, provided that the interaction strength mu is smaller than a critical value. The saddle index n_s is equal to alpha_0 and its distribution function has a maximum at n_s^max = 1/3. The density p(e) of stationary points with energy per particle e, as well as the Euler characteristic chi(e), are singular at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu) \neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per particle at the thermodynamic phase transition point T_c. This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H \neq 0. The average saddle index bar{n}_s as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 > upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure

Isentropic Curves at Magnetic Phase Transitions

Experiments on cold atom systems in which a lattice potential is ramped up on a confined cloud have raised intriguing questions about how the temperature varies along isentropic curves, and how these curves intersect features in the phase diagram. In this paper, we study the isentropic curves of two models of magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods are used. The isentropic curves of the BCM generally run parallel to the phase boundary in the Ising regime of low vacancy density, but intersect the phase boundary when the magnetic transition is mainly driven by a proliferation of vacancies. Adiabatic heating occurs in moving away from the phase boundary. The isentropes of the half-filled FHM have a relatively simple structure, running parallel to the temperature axis in the paramagnetic phase, and then curving upwards as the antiferromagnetic transition occurs. However, in the doped case, where two magnetic phase boundaries are crossed, the isentrope topology is considerably more complex