335 research outputs found
Weak value of Dwell time for Quantum Dissipative spin-1/2 System
The dwell time is calculated within the framework of time dependent weak
measurement considering dissipative interaction between a spin half system and
the environment. Caldirola and Montaldi's method of retarded Schroedinger
equation is used to study the dissipative system. The result shows that
inclusion of dissipative interaction prevents zero time tunneling.Comment: This work is original. arXiv admin note: text overlap with
arXiv:0807.1357, arXiv:quant-ph/9611018, arXiv:quant-ph/9501015 by other
author
Transferring elements of a density matrix
We study restrictions imposed by quantum mechanics on the process of matrix
elements transfer. This problem is at the core of quantum measurements and
state transfer. Given two systems \A and \B with initial density matrices
and , respectively, we consider interactions that lead to
transferring certain matrix elements of unknown into those of the
final state of \B. We find that this process eliminates the
memory on the transferred (or certain other) matrix elements from the final
state of \A. If one diagonal matrix element is transferred, , the memory on each non-diagonal element
is completely eliminated from the final density operator of
\A. Consider the following three quantities \Re \la_{a\not =b}, \Im
\la_{a\not =b} and \la_{aa}-\la_{bb} (the real and imaginary part of a
non-diagonal element and the corresponding difference between diagonal
elements). Transferring one of them, e.g., \Re\tir_{a\not = b}=\Re\la_{a\not =
b}, erases the memory on two others from the final state of \A.
Generalization of these set-ups to a finite-accuracy transfer brings in a
trade-off between the accuracy and the amount of preserved memory. This
trade-off is expressed via system-independent uncertainty relations which
account for local aspects of the accuracy-disturbance trade-off in quantum
measurements.Comment: 9 pages, 2 table
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
The Physical Principles of Quantum Mechanics. A critical review
The standard presentation of the principles of quantum mechanics is
critically reviewed both from the experimental/operational point and with
respect to the request of mathematical consistency and logical economy. A
simpler and more physically motivated formulation is discussed. The existence
of non commuting observables, which characterizes quantum mechanics with
respect to classical mechanics, is related to operationally testable
complementarity relations, rather than to uncertainty relations. The drawbacks
of Dirac argument for canonical quantization are avoided by a more geometrical
approach.Comment: Bibliography and section 2.1 slightly improve
Information and noise in quantum measurement
Even though measurement results obtained in the real world are generally both
noisy and continuous, quantum measurement theory tends to emphasize the ideal
limit of perfect precision and quantized measurement results. In this article,
a more general concept of noisy measurements is applied to investigate the role
of quantum noise in the measurement process. In particular, it is shown that
the effects of quantum noise can be separated from the effects of information
obtained in the measurement. However, quantum noise is required to ``cover up''
negative probabilities arising as the quantum limit is approached. These
negative probabilities represent fundamental quantum mechanical correlations
between the measured variable and the variables affected by quantum noise.Comment: 16 pages, short comment added in II.B., final version for publication
in Phys. Rev.
Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures
In this paper, we provide a representation theory for the Feynman operator
calculus. This allows us to solve the general initial-value problem and
construct the Dyson series. We show that the series is asymptotic, thus proving
Dyson's second conjecture for QED. In addition, we show that the expansion may
be considered exact to any finite order by producing the remainder term. This
implies that every nonperturbative solution has a perturbative expansion. Using
a physical analysis of information from experiment versus that implied by our
models, we reformulate our theory as a sum over paths. This allows us to relate
our theory to Feynman's path integral, and to prove Dyson's first conjecture
that the divergences are in part due to a violation of Heisenberg's uncertainly
relations
From Einstein's Theorem to Bell's Theorem: A History of Quantum Nonlocality
In this Einstein Year of Physics it seems appropriate to look at an important
aspect of Einstein's work that is often down-played: his contribution to the
debate on the interpretation of quantum mechanics. Contrary to popular opinion,
Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the
claimed completeness of orthodox quantum mechanics. I suggest that Einstein's
argument, as stated most clearly in 1946, could justly be called Einstein's
reality-locality-completeness theorem, since it proves that one of these three
must be false. Einstein's instinct was that completeness of orthodox quantum
mechanics was the falsehood, but he failed in his quest to find a more complete
theory that respected reality and locality. Einstein's theorem, and possibly
Einstein's failure, inspired John Bell in 1964 to prove his reality-locality
theorem. This strengthened Einstein's theorem (but showed the futility of his
quest) by demonstrating that either reality or locality is a falsehood. This
revealed the full nonlocality of the quantum world for the first time.Comment: 18 pages. To be published in Contemporary Physics. (Minor changes;
references and author info added
Finite size corrections to scaling in high Reynolds number turbulence
We study analytically and numerically the corrections to scaling in
turbulence which arise due to the finite ratio of the outer scale of
turbulence to the viscous scale , i.e., they are due to finite size
effects as anisotropic forcing or boundary conditions at large scales. We find
that the deviations \dzm from the classical Kolmogorov scaling of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m}
decrease like . Our numerics employ a
reduced wave vector set approximation for which the small scale structures are
not fully resolved. Within this approximation we do not find independent
anomalous scaling within the inertial subrange. If anomalous scaling in the
inertial subrange can be verified in the large limit, this supports the
suggestion that small scale structures should be responsible, originating from
viscosity either in the bulk (vortex tubes or sheets) or from the boundary
layers (plumes or swirls)
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
Quantum State Reconstruction of Many Body System Based on Complete Set of Quantum Correlations Reduced by Symmetry
We propose and study a universal approach for the reconstruction of quantum
states of many body systems from symmetry analysis. The concept of minimal
complete set of quantum correlation functions (MCSQCF) is introduced to
describe the state reconstruction. As an experimentally feasible physical
object, the MCSQCF is mathematically defined through the minimal complete
subspace of observables determined by the symmetry of quantum states under
consideration. An example with broken symmetry is analyzed in detail to
illustrate the idea.Comment: 10 pages, n figures, Revte
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