420 research outputs found

### 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

### 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

### 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)âŠ—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

### 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

### 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 Machâ€“Zehnder interferometer is discussed to show the emergence of nonclassical regions, characterized by negative values of Mandelâ€™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

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