Quantumness beyond quantum mechanics

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunneling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is though within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).Comment: 11 pages, 4 figures; based on a talk at the Conference "Emergent Quantum Mechanics" / 5th Heinz von Foerster Congress (Vienna, Nov 11-13, 2011

Quantum Zeno-based control mechanism for molecular fragmentation

A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br$_2$ complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three dimensional wave packet simulations are carried out by using ab initio interaction potentials recently obtained to reproduce available experimental data. Two numerical models to simulate the repeated measurements are reported and analyzed. It is found that the otherwise fast vibrational predissociation is slowed down in favor of the slow electronic (double fragmentation) predissociation, which is enhanced by several orders of magnitude. Based on these theoretical predictions, some hints to experimentalists to confirm their validity are also proposed.Comment: 4 pages, 3 figure

Importance Sampling: Intrinsic Dimension and Computational Cost

The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.Comment: Statistical Scienc

Vibrational effects in the quantum dynamics of the H + D_2^+ charge transfer reaction

The H + D_2^+(v=0,1 and 2) charge transfer reaction is studied using an accurate wave packet method, using recently proposed coupled diabatic potential energy surfaces. The state-to-state cross section is obtained for three different channels: non-reactive charge transfer, reactive charge transfer, and exchange reaction. The three processes proceed via the electronic transition from the first excited to the ground electronic state. The cross section for the three processes increases with the initial vibrational excitation. The non-reactive charge transfer process is the dominant channel, whose branching ratio increases with collision energy, and it compares well with experimental measurements at collision energies around 0.5 eV. For lower energies the experimental cross section is considerably higher, suggesting that it corresponds to higher vibrational excitation of D_2^+(v) reactants. Further experimental studies of this reaction and isotopic variants are needed, where conditions are controlled to obtain a better analysis of the vibrational effects of the D_2^+ reagents.Comment: 15 pages, 7 figure

Quantum Zeno effect: Quantum shuffling and Markovianity

The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.Comment: 12 pages, 2 figure

Nanoimaging of Organic Charge Retention Effects: Implications for Nonvolatile Memory, Neuromorphic Computing, and High Dielectric Breakdown Devices

While a large variety of organic and molecular materials have been found to exhibit charge memory effects, the underlying mechanism is not well-understood, which hinders rational device design. Here, we study the charge retention mechanism of a nanoscale memory system, an organic monolayer on a silicon substrate, with Au nanoparticles on top serving as the electrical contact. Combining scanning probe imaging/manipulation and density functional simulations, we observe stable charge retention effects in the system and attributed it to polaron effects at the amine functional groups. Our findings can pave the way for applications in nonvolatile memory, neuromorphic computing, and high dielectric breakdown devices

Matrix Product States: Symmetries and Two-Body Hamiltonians

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.Comment: PDFLatex, 12 pages and 6 figure

Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations

We consider a 2-dimensional system of linear ordinary differential equations whose coefficients are definable in an o-minimal structure R. We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of R by all solutions at 0 of the system is o-minimal. We also show that if the coefficients of the system have a Taylor development of sufficiently large finite order, then the question of which of the two cases holds can be effectively determined in terms of the coefficients of this Taylor development.Second author was partially supported by Ministerio de Ciencia e Innovacióna, Spain, process MTM2010-1547