Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space

The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.Comment: 34 page

Ancient Yersinia pestis and Salmonella enterica genomes from Bronze Age Crete

During the late 3rd millennium BCE, the Eastern Mediterranean and Near East witnessed societal changes in many regions, which are usually explained with a combination of social and climatic factors.1, 2, 3, 4 However, recent archaeogenetic research forces us to rethink models regarding the role of infectious diseases in past societal trajectories.5 The plague bacterium Yersinia pestis, which was involved in some of the most destructive historical pandemics,5, 6, 7, 8 circulated across Eurasia at least from the onset of the 3rd millennium BCE,9, 10, 11, 12, 13 but the challenging preservation of ancient DNA in warmer climates has restricted the identification of Y. pestis from this period to temperate climatic regions. As such, evidence from culturally prominent regions such as the Eastern Mediterranean is currently lacking. Here, we present genetic evidence for the presence of Y. pestis and Salmonella enterica, the causative agent of typhoid/enteric fever, from this period of transformation in Crete, detected at the cave site Hagios Charalambos. We reconstructed one Y. pestis genome that forms part of a now-extinct lineage of Y. pestis strains from the Late Neolithic and Bronze Age that were likely not yet adapted for transmission via fleas. Furthermore, we reconstructed two ancient S. enterica genomes from the Para C lineage, which cluster with contemporary strains that were likely not yet fully host adapted to humans. The occurrence of these two virulent pathogens at the end of the Early Minoan period in Crete emphasizes the necessity to re-introduce infectious diseases as an additional factor possibly contributing to the transformation of early complex societies in the Aegean and beyond.Results and discussion STAR★Method

Classical Vs Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modelled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the "which way" experiments); they are, however, distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in Found. Phy

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to appear in Foundations of Physic

Quantum Equilibrium and the Origin of Absolute Uncertainty

The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr\"odinger's equation for a system of particles when we merely insist that ``particles'' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an {\it appearance} of randomness emerges, precisely as described by the quantum formalism and given, for example, by ``\rho=|\psis|^2.'' A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.Comment: 75 pages. This paper was published a long time ago, but was never archived. We do so now because it is basic for our recent article quant-ph/0308038, which can in fact be regarded as an appendix of the earlier on

Thermal Particle and Photon Production in Pb+Pb Collisions with Transverse Flow

Particle and photon production is analyzed in the presence of transverse flow using two approximations to describe the properties of the hadronic medium, one containing only $\pi, \rho, \omega$, and $\eta$ mesons (simplified equation of state) and the other containing hadrons and resonances from the particle data table. Both are considered with and without initial quark gluon plasma formation. In each case the initial temperature is fixed by requiring $dN_{ch}/dy \sim$ 550 in the final state. It is shown that most observables are very sensitive to the equation of state. This is particularly evident when comparing the results of the simplified equation of state in the scenarios with and without phase transition. The hadronic gas scenario leads to a substantially higher rate for the $p_T$-distribution of all particles. In the complete equation of state with several hundreds of hadronic resonances, the difference between the scenarios with and without phase transition is rather modest. Both photon and particle spectra, in a wide $p_T$ range, show very similar behavior. It is therefore concluded that from the $p_T$ spectra it will be hard to disentangle quark gluon plasma formation in the initial state. It is to be stressed however, that there are conceptual difficulties in applying a pure hadronic gas equation of state at SPS-energies. The phase transition scenario with a quark gluon plasma present in the initial state seems to be the more natural one.Comment: 9 pages RevTeX figures in postscript forma

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Contextual-value approach to the generalized measurement of observables

We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104 240401 (2010)]. The theory of contextual values extends the well-established theory of generalized state measurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable construction, detector coupling, generalized measurement, and measurement disturbance. We then extend the results to quantum probability theory built as a superstructure on the classical theory, pointing out both the classical correspondences to and the full quantum generalizations of both L\"uder's rule and the Aharonov-Bergmann-Lebowitz rule in the process. We find in both cases that the contextual values of a system observable form a generalized spectrum that is associated with the independent outcomes of a partially correlated and generally ambiguous detector; the eigenvalues are a special case when the detector is perfectly correlated and unambiguous. To illustrate the approach, we apply the technique to both a classical example of marble color detection and a quantum example of polarization detection. For the quantum example we detail two devices: Fresnel reflection from a glass coverslip, and continuous beam displacement from a calcite crystal. We also analyze the three-box paradox to demonstrate that no negative probabilities are necessary in its analysis. Finally, we provide a derivation of the quantum weak value as a limit point of a pre- and postselected conditioned average and provide sufficient conditions for the derivation to hold.Comment: 36 pages, 5 figures, published versio

To quantum mechanics through random fluctuations at the Planck time scale

We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the asymptotic expansion of classical statistical averages with respect to a small parameter $\alpha.$ Therefore statistical predictions of QM are only approximative and a better precision of measurements would induce deviations of experimental averages from quantum mechanical ones. In this note we present a natural physical interpretation of $\alpha$ as the time scaling parameter (between quantum and prequantum times). By considering the Planck time $t_P$ as the unit of the prequantum time scale we couple our prequantum model with studies on the structure of space-time on the Planck scale performed in general relativity, string theory and cosmology. In our model the Planck time $t_P$ is not at all the {\it "ultimate limit to our laws of physics"} (in the sense of laws of classical physics). We study random (Gaussian) infinite-dimensional fluctuations for prequantum times $s\leq t_P$ and show that quantum mechanical averages can be considered as an approximative description of such fluctuations.Comment: Discussion on the possibility to go beyond Q