58 research outputs found
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
Bohmian mechnaics is the most naively obvious embedding imaginable of
Schr\"odingers's equation into a completely coherent physical theory. It
describes a world in which particles move in a highly non-Newtonian sort of
way, one which may at first appear to have little to do with the spectrum of
predictions of quantum mechanics. It turns out, however, that as a consequence
of the defining dynamical equations of Bohmian mechanics, when a system has
wave function its configuration is typically random, with probability
density given by , the quantum equilibrium distribution. It
also turns out that the entire quantum formalism, operators as observables and
all the rest, naturally emerges in Bohmian mechanics from the analysis of
``measurements.'' This analysis reveals the status of operators as observables
in the description of quantum phenomena, and facilitates a clear view of the
range of applicability of the usual quantum mechanical formulas.Comment: 77 page
Bohmian Mechanics and the Meaning of the Wave Function
We outline how Bohmian mechanics works: how it deals with various issues in
the foundations of quantum mechanics and how it is related to the usual quantum
formalism. We then turn to some objections to Bohmian mechanics, for example
the fact that in Bohmian mechanics there is no back action of particle
configurations upon wave functions. These lead us to our main concern: a more
careful consideration of the meaning of the wave function in quantum mechanics,
as suggested by a Bohmian perspective. We propose that the reason, on the
universal level, that there is no action of configurations upon wave functions,
as there seems to be between all other elements of physical reality, is that
the wave function of the universe is not an element of physical reality. We
propose that the wave function belongs to an altogether different category of
existence than that of substantive physical entities, and that its existence is
nomological rather than material. We propose, in other words, that the wave
function is a component of physical law rather than of the reality described by
the law.Comment: 15 pages, LaTeX, 1 figure, contribution to ``Experimental
Metaphysics---Quantum Mechanical Studies in Honor of Abner Shimony,'' edited
by R.S.Cohen, M. Horne, and J. Stachel, Boston Studies in the Philosophy of
Science (Kluwer, 1996
Reality and the Role of the Wavefunction in Quantum Theory
The most puzzling issue in the foundations of quantum mechanics is perhaps
that of the status of the wave function of a system in a quantum universe. Is
the wave function objective or subjective? Does it represent the physical state
of the system or merely our information about the system? And if the former,
does it provide a complete description of the system or only a partial
description? We shall address these questions here mainly from a Bohmian
perspective, and shall argue that part of the difficulty in ascertaining the
status of the wave function in quantum mechanics arises from the fact that
there are two different sorts of wave functions involved. The most fundamental
wave function is that of the universe. From it, together with the configuration
of the universe, one can define the wave function of a subsystem. We argue that
the fundamental wave function, the wave function of the universe, has a
law-like character.Comment: 23 page
Naive Realism about Operators
A source of much difficulty and confusion in the interpretation of quantum
mechanics is a ``naive realism about operators.'' By this we refer to various
ways of taking too seriously the notion of operator-as-observable, and in
particular to the all too casual talk about ``measuring operators'' that occurs
when the subject is quantum mechanics. Without a specification of what should
be meant by ``measuring'' a quantum observable, such an expression can have no
clear meaning. A definite specification is provided by Bohmian mechanics, a
theory that emerges from Sch\"rodinger's equation for a system of particles
when we merely insist that ``particles'' means particles. Bohmian mechanics
clarifies the status and the role of operators as observables in quantum
mechanics by providing the operational details absent from standard quantum
mechanics. It thereby allows us to readily dismiss all the radical claims
traditionally enveloping the transition from the classical to the quantum
realm---for example, that we must abandon classical logic or classical
probability. The moral is rather simple: Beware naive realism, especially about
operators!Comment: 18 pages, LaTex2e with AMS-LaTeX, to appear in Erkenntnis, 1996 (the
proceedings of the international conference ``Probability, Dynamics and
Causality,'' Luino, Italy, 15-17 June 1995, a special issue edited by D.
Costantini and M.C. Gallavotti and dedicated to Prof. R. Jeffrey
How does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?
Bohmian mechanics is a theory that provides a consistent explanation of
quantum phenomena in terms of point particles whose motion is guided by the
wave function. In this theory, the state of a system of particles is defined by
the actual positions of the particles and the wave function of the system; and
the state of the system evolves deterministically. Thus, the Bohmian state can
be compared with the state in classical mechanics, which is given by the
positions and momenta of all the particles, and which also evolves
deterministically. However, while in classical mechanics it is usually taken
for granted and considered unproblematic that the state is, at least in
principle, measurable, this is not the case in Bohmian mechanics. Due to the
linearity of the quantum dynamical laws, one essential component of the Bohmian
state, the wave function, is not directly measurable. Moreover, it turns out
that the measurement of the other component of the state -the positions of the
particles- must be mediated by the wave function; a fact that in turn implies
that the positions of the particles, though measurable, are constrained by
absolute uncertainty. This is the key to understanding how Bohmian mechanics,
despite being deterministic, can account for all quantum predictions, including
quantum randomness and uncertainty.Comment: To appear in Fluctuation and Noise Letters special issue "Quantum and
classical frontiers of noise
Fidelity optimization for holonomic quantum gates in dissipative environments
We analyze the performance of holonomic quantum gates in semi-conductor
quantum dots, driven by ultrafast lasers, under the effect of a dissipative
environment. In agreement with the standard practice, the environment is
modeled as a thermal bath of oscillators linearly coupled with the excitonic
states of the quantum dot. Standard techniques of quantum dissipation make the
problem amenable to a numerical treatment and allow to determine the fidelity
(the common gate-performance estimator), as a function of all the relevant
physical parameters. As a consequence of our analysis, we show that, by varying
in a suitable way the controllable parameters, the disturbance of the
environment can be (approximately) suppressed, and the performance of the gate
optimized--provided that the thermal bath is purely superhomic. We conclude by
showing that such an optimization it is impossible for ohmic environments.Comment: 5 pages, 4 figures, Revtex4. v2: Minor changes, Corrected typos and
Added reference
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