Statistical Properties of Strongly Correlated Quantum LiquidsRistig, M.; Gernoth, K.
doi: 10.1007/s10701-009-9370-1pmid: N/A
Modern microscopic theory is employed to construct a powerful analytical algorithm that permits a clear description of characteristic features of strongly correlated quantum fluids in thermodynamic equilibrium. Using recently developed formal results we uncover an intricate relationship between strongly correlated systems and free quantum gases of appropriately defined constituents. The latter entities are precisely defined renormalized bosons or fermions. They carry all the information contained in the statistical correlations of the strongly interacting many-particle system by virtue of their effective masses. The mass of such a renormalized boson or fermion depends in a specific form on temperature, bulk particle number density of the many-body system, and eventually on momentum. Due to these properties the renormalized bosons and fermions determine in particular the location and nature of the transition to non-normal phases.
Time in Quantum Physics: From an External Parameter to an Intrinsic ObservableBrunetti, Romeo; Fredenhagen, Klaus; Hoge, Marc
doi: 10.1007/s10701-009-9400-zpmid: N/A
In the Schrödinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schrödinger equation give rise to weights on the enlarged algebra of observables. States in the associated GNS representation correspond to states on the original algebra composed with a completely positive unit preserving map. Application of this map to the functions of the time operator on the large system delivers the positive operator valued maps which were previously proposed by two of us as time observables. As an example we discuss the application of this formalism to the Wheeler-DeWitt theory of a scalar field on a Robertson-Walker spacetime.
On the Complementarity of the Quadrature ObservablesLahti, Pekka; Pellonpää, Juha-Pekka
doi: 10.1007/s10701-009-9373-ypmid: N/A
In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.
Quantum Discreteness is an IllusionZeh, H.
doi: 10.1007/s10701-009-9383-9pmid: N/A
I review arguments demonstrating how the concept of “particle” numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number (“momentum”) characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines a non-degenerate “n-particle wave function”. Other discrete properties and phenomena (such as particle positions and “events”) can be understood by means of the fast but continuous process of decoherence: the irreversible dislocalization of superpositions. Any wave-particle dualism thus becomes obsolete. The observation of individual outcomes of this decoherence process in measurements requires either a subsequent collapse of the wave function or a “branching observer” in accordance with the Schrödinger equation—both possibilities applying clearly after the decoherence process. Any probability interpretation of the wave function in terms of local elements of reality, such as particles or other classical concepts, would open a Pandora’s box of paradoxes, as is illustrated by various misnomers that have become popular in quantum theory.
On the Structure of Pseudo BL-algebras and Pseudo Hoops in Quantum LogicsDvurečenskij, A.; Giuntini, R.; Kowalski, T.
doi: 10.1007/s10701-009-9342-5pmid: N/A
The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo hoop can be embedded into the negative cone of the reals. We give an equational base characterizing representable pseudo hoops. We also describe some subvarieties: normal-valued, and varieties where each maximal filter is normal. We produce some noncommutative covers and extend the area where each algebra is good. Finally, we show that there are uncountably many subvarieties of pseudo BL-algebras having members that are not good.
Type-Decomposition of an Effect AlgebraFoulis, David; Pulmannová, Sylvia
doi: 10.1007/s10701-009-9344-3pmid: N/A
Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.
Effect Algebras Are Not Adequate Models forQuantum MechanicsGudder, Stan
doi: 10.1007/s10701-009-9369-7pmid: N/A
We show that an effect algebra E possess an order-determining set of states if and only if E is semiclassical; that is, E is essentially a classical effect algebra. We also show that if E possesses at least one state, then E admits hidden variables in the sense that E is homomorphic to an MV-algebra that reproduces the states of E. Both of these results indicate that we cannot distinguish between a quantum mechanical effect algebra and a classical one. Hereditary properties of sharpness and coexistence are discussed and the existence of {0,1} and dispersion-free states are considered. We then discuss a stronger structure called a sequential effect algebra (SEA) that we believe overcomes some of the inadequacies of an effect algebra. We show that a SEA is semiclassical if and only if it possesses an order-determining set of dispersion-free states.
Physics and CausationEsfeld, Michael
doi: 10.1007/s10701-009-9357-ypmid: N/A
The paper makes a case for there being causation in the form of causal properties or causal structures in the domain of fundamental physics. That case is built in the first place on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties, GRW being the most elaborate physical proposal for such an interpretation. I then argue that the interpretation that goes back to Everett can also be read in a causal manner, the splitting of the world being conceivable as a causal process. Finally, I mention that the way in which general relativity theory conceives the metrical field opens up the way for a causal conception of the metrical properties as well.