Related papers: Statistics and Quantum Group Symmetries
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Symmetries are of fundamental interest in many areas of science. In quantum information theory, if a quantum state is invariant under permutations of its subsystems, it is a well-known and widely used result that its marginal can be…
We initiate a general approach to the relative braid group symmetries on (universal) $\imath$quantum groups, arising from quantum symmetric pairs of arbitrary finite types, and their modules. Our approach is built on new intertwining…
We study the canonical problem of a Fermi gas interacting with a weakly repulsive Bose-Einstein condensate at zero temperature. To explore the quantum phases across the full range of boson-fermion interactions, we construct a versatile…
Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction…
We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. Our previous work has built a relativistic quantum field theory which allows interactions involving infinite…
Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein…
The problem of quantum state estimation is crucial in the development of quantum technologies. In particular, the use of symmetric quantum states is useful in many relevant applications. In this work, we analyze the task of reconstructing…
Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems and to provide solutions equivalent to the Bethe ansatz. The method is illustrated on the 1D Heisenberg ferromagnet whose symmetry…
We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple…
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution…
We have analytically obtained 1-particle density matrices for ideal Bose and Fermi gases in both the 3-D box geometries and the harmonically trapped geometries for the entire range of temperature. We have obtained quantum cluster expansions…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
For almost two decades, it has been believed that the quantum statistical properties of bosons are preserved in plasmonic systems. This idea has been stimulated by experimental work reporting the possibility of preserving nonclassical…
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
We theoretically examine equilibrium properties of the harmonically trapped ideal Bose and Fermi gases in the quantum degeneracy regime. We analyze thermodynamic characteristics of gases with a finite number of atoms by means of the known…
We apply the general construction of a twist of bigraded Hopf algebras by skew bicharacters to obtain two-parameter quantum groups in the Drinfeld-Jimbo, new Drinfeld (for affine types), and FRT (for both finite and affine) presentations…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…