112 research outputs found
Time of Arrival from Bohmian Flow
We develop a new conception for the quantum mechanical arrival time
distribution from the perspective of Bohmian mechanics. A detection probability
for detectors sensitive to quite arbitrary spacetime domains is formulated.
Basic positivity and monotonicity properties are established. We show that our
detection probability improves and generalises earlier proposals by Leavens and
McKinnon. The difference between the two notions is illustrated through
application to a free wave packet.Comment: 18 pages, 8 figures, to appear in Journ. Phys. A; representation of
ref. 5 improved (thanks to Rick Leavens
Hypersurface Bohm-Dirac models
We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio
Times of arrival: Bohm beats Kijowski
We prove that the Bohmian arrival time of the 1D Schroedinger evolution
violates the quadratic form structure on which Kijowski's axiomatic treatment
of arrival times is based. Within Kijowski's framework, for a free right moving
wave packet, the various notions of arrival time (at a fixed point x on the
real line) all yield the same average arrival time. We derive an inequality
relating the average Bohmian arrival time to the one of Kijowksi. We prove that
the average Bohmian arrival time is less than Kijowski's one if and only if the
wave packet leads to position probability backflow through x. Otherwise the two
average arrival times coincide.Comment: 9 page
Locality and Causality in Hidden Variables Models of Quantum Theory
Motivated by Popescu's example of hidden nonlocality, we elaborate on the
conjecture that quantum states that are intuitively nonlocal, i.e., entangled,
do not admit a local causal hidden variables model. We exhibit quantum states
which either (i) are nontrivial counterexamples to this conjecture or (ii)
possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we
propose a nonlocality complexity classification scheme suggested by the latter
possibility. Furthermore, we show that Werner's (and similar) hidden variables
models can be extended to an important class of generalized observables.
Finally a result of Fine on the equivalence of stochastic and deterministic
hidden variables is generalized to causal models.Comment: revised version, 21 pages, submitted to Physical Review
Non-Locality and Theories of Causation
The aim of the paper is to investigate the characterization of an unambiguous
notion of causation linking single space-llike separated events in EPR-Bell
frameworks. This issue is investigated in ordinary quantum mechanics, with some
hints to no collapse formulations of the theory such as Bohmian mechanics.Comment: Presented at the NATO Advanced Research Workshop on Modality,
Probability and Bell's Theorems, Cracow, Poland, August 19-23, 200
Quantitative estimates of discrete harmonic measures
A theorem of Bourgain states that the harmonic measure for a domain in
is supported on a set of Hausdorff dimension strictly less than
\cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the
distribution of the first entrance point of a random walk into a subset of , . By refining the argument, we prove that for all \b>0 there
exists \rho (d,\b)N(d,\b), any , and any | \{y\in\Z^d\colon \nu_{A,x}(y)
\geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where denotes the
probability that is the first entrance point of the simple random walk
starting at into . Furthermore, must converge to as \b \to
\infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne
Efficient Set Sharing Using ZBDDs
Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time
Bohmian transmission and reflection dwell times without trajectory sampling
Within the framework of Bohmian mechanics dwell times find a straightforward
formulation. The computation of associated probabilities and distributions
however needs the explicit knowledge of a relevant sample of trajectories and
therefore implies formidable numerical effort. Here a trajectory free
formulation for the average transmission and reflection dwell times within
static spatial intervals [a,b] is given for one-dimensional scattering
problems. This formulation reduces the computation time to less than 5% of the
computation time by means of trajectory sampling.Comment: 14 pages, 7 figures; v2: published version, significantly revised and
shortened (former sections 2 and 3 omitted, appendix A added, simplified
mathematics
On the exit statistics theorem of many particle quantum scattering
We review the foundations of the scattering formalism for one particle
potential scattering and discuss the generalization to the simplest case of
many non interacting particles. We point out that the "straight path motion" of
the particles, which is achieved in the scattering regime, is at the heart of
the crossing statistics of surfaces, which should be thought of as detector
surfaces. We sketch a proof of the relevant version of the many particle flux
across surfaces theorem and discuss what needs to be proven for the foundations
of scattering theory in this context.Comment: 15 pages, 4 figures; to appear in the proceedings of the conference
"Multiscale methods in Quantum Mechanics", Accademia dei Lincei, Rome,
December 16-20, 200
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