Time Operator, Real Tunneling Time in Strong Field Interaction and the Attoclock

Attosecond science, beyond its importance from application point of view, is of a fundamental interest in physics. The measurement of tunneling time in attosecond experiments offers a fruitful opportunity to understand the role of time in quantum mechanics. In the present work, we show that our real T-time relation derived in earlier works can be derived from an observable or a time operator, which obeys an ordinary commutation relation. Moreover, we show that our real T-time can also be constructed, inter alia, from the well-known Aharonov–Bohm time operator. This shows that the specific form of the time operator is not decisive, and dynamical time operators relate identically to the intrinsic time of the system. It contrasts the famous Pauli theorem, and confirms the fact that time is an observable, i.e., the existence of time operator and that the time is not a parameter in quantum mechanics. Furthermore, we discuss the relations with different types of tunneling times, such as Eisenbud–Wigner time, dwell time, and the statistically or probabilistic defined tunneling time. We conclude with the hotly debated interpretation of the attoclock measurement and the advantage of the real T-time picture versus the imaginary one.

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Tunneling Time in Attosecond Experiments and Time Operator in Quantum Mechanics

Mathematics ◽

10.3390/math6100192 ◽

2018 ◽

Vol 6 (10) ◽

pp. 192

Author(s):

Ossama Kullie

Keyword(s):

Experimental Data ◽

Quantum Mechanics ◽

Time Operator ◽

Tunneling Time ◽

Barrier Width ◽

Time Model ◽

Tunneling Model ◽

Misleading Interpretation ◽

Aharonov Bohm

Attosecond science is of a fundamental interest in physics. The measurement of the tunneling time in attosecond experiments, offers a fruitful opportunity to understand the role of time in quantum mechanics (QM). We discuss in this paper our tunneling time model in relation to two time operator definitions introduced by Bauer and Aharonov–Bohm. We found that both definitions can be generalized to the same type of time operator. Moreover, we found that the introduction of a phenomenological parameter by Bauer to fit the experimental data is unnecessary. The issue is resolved with our tunneling model by considering the correct barrier width, which avoids a misleading interpretation of the experimental data. Our analysis shows that the use of the so-called classical barrier width, to be precise, is incorrect.

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Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

International Journal of Modern Physics A ◽

10.1142/s0217751x20501146 ◽

2020 ◽

Vol 35 (21) ◽

pp. 2050114

Author(s):

M. Bauer ◽

C. A. Aguillón ◽

G. E. García

Keyword(s):

Quantum Mechanics ◽

Quantum Gravity ◽

Relativistic Quantum ◽

Canonical Quantization ◽

Time Operator ◽

Relativistic Quantum Mechanics ◽

Problem Of Time ◽

Quantization Of Gravity ◽

Dynamical Time ◽

Spatial Coordinates

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

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A dynamical time operator in Dirac's relativistic quantum mechanics

International Journal of Modern Physics A ◽

10.1142/s0217751x14500365 ◽

2014 ◽

Vol 29 (06) ◽

pp. 1450036 ◽

Cited By ~ 18

Author(s):

M. Bauer

Keyword(s):

Quantum Mechanics ◽

Wave Packet ◽

Phase Velocity ◽

Relativistic Quantum ◽

Rate Of Change ◽

Time Operator ◽

Relativistic Quantum Mechanics ◽

Instantaneous Rate ◽

Expectation Value ◽

Dynamical Time

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

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de Broglie clock, electron channeling, and time in quantum mechanics

Canadian Journal of Physics ◽

10.1139/cjp-2017-0571 ◽

2019 ◽

Vol 97 (1) ◽

pp. 37-41 ◽

Cited By ~ 1

Author(s):

M. Bauer

Keyword(s):

Quantum Mechanics ◽

Relativistic Quantum ◽

Resonance Energy ◽

Intrinsic Property ◽

Theoretical Description ◽

Time Operator ◽

Relativistic Quantum Mechanics ◽

Electron Channeling ◽

Quantum Mechanical Description ◽

Dynamical Time

De Broglie’s association of a wave to particles is a fundamental concept in the quantum mechanical description of nature. The wave oscillation is referred to alternatively as the “de Broglie clock”, the “Compton clock”, or the “de Broglie periodic phenomenon”. In the present paper it is shown that Dirac’s relativistic quantum mechanics, complemented with the dynamical time operator recently introduced, provides a consistent theoretical description of: (i) the generation of the de Broglie wave through Lorentz boosts; and (ii) the characteristics of the resonance observed in electron channeling through thin crystals as responding to both the periodicity derived from the adjustment of the de Broglie period to the crystal interatomic distance (resonance energy) and the periodicity of the predicted trembling motion (Zitterbewegung). One can conclude that the channeling experiments provide the first direct evidence of the electron Zitterbewegung, and that the de Broglie period is an intrinsic property of matter arising from a self-adjoint dynamical time operator.

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QUANTUM MECHANICS AND THE ROLE OF TIME: ARE QUANTUM SYSTEMS MARKOVIAN?

International Journal of Modern Physics B ◽

10.1142/s0217979212430059 ◽

2012 ◽

Vol 26 (27n28) ◽

pp. 1243005 ◽

Cited By ~ 2

Author(s):

THOMAS DURT

Keyword(s):

Quantum Mechanics ◽

Quantum Systems ◽

Quantum Nonlocality ◽

Border Line ◽

The Past ◽

Open Questions ◽

The Status ◽

Alternative Theories ◽

Time In Quantum Mechanics

The predictions of the Quantum Theory have been verified so far with astonishingly high accuracy. Despite of its impressive successes, the theory still presents mysterious features such as the border line between the classical and quantum world, or the deep nature of quantum nonlocality. These open questions motivated in the past several proposals of alternative and/or generalized approaches. We shall discuss in the present paper alternative theories that can be infered from a reconsideration of the status of time in quantum mechanics. Roughly speaking, quantum mechanics is usually formulated as a memory free (Markovian) theory at a fundamental level, but alternative, nonMarkovian, formulations are possible, and some of them can be tested in the laboratory. In our paper we shall give a survey of these alternative proposals, describe related experiments that were realized in the past and also formulate new experimental proposals.

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TIME IN RELATIVISTIC AND NONRELATIVISTIC QUANTUM MECHANICS

International Journal of Quantum Information ◽

10.1142/s021974990900516x ◽

2009 ◽

Vol 07 (03) ◽

pp. 595-602 ◽

Cited By ~ 11

Author(s):

HRVOJE NIKOLIĆ

Keyword(s):

Quantum Mechanics ◽

Time Operator ◽

Position Operator ◽

Nonrelativistic Quantum ◽

Time Dynamics ◽

Bell Theorem ◽

Time Position ◽

Nonrelativistic Quantum Mechanics ◽

Bohmian Interpretation

The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The space–time position operator acts in the Hilbert space of functions of space and time. Dynamics, however, makes eigenstates of the time operator unphysical. This poses a problem for the standard interpretation of QM and reinforces the role of alternative interpretations such as the Bohmian one. The Bohmian interpretation, despite of being nonlocal in accordance with the Bell theorem, is shown to be relativistic covariant.

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DISSIPATIVE QUANTUM MECHANICS AND KONDO-LIKE IMPURITIES ON NONCOMMUTATIVE TWO-TORI

International Journal of Modern Physics A ◽

10.1142/s0217751x12500078 ◽

2012 ◽

Vol 27 (02) ◽

pp. 1250007

Author(s):

PATRIZIA IACOMINO ◽

VINCENZO MAROTTA ◽

ADELE NADDEO

Keyword(s):

Field Theory ◽

Quantum Mechanics ◽

Quantum Hall ◽

Point Of View ◽

Massless Scalar ◽

Conformal Field ◽

Boundary Interaction ◽

New Evidence ◽

The Relationship

In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a general one-to-one correspondence between the m-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings1,2[Formula: see text] and an Abelian noncommutative field theory (NCFT) has been established.3 That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids.4 On the other hand, the m-reduced CFT is equivalent to a system of two massless scalar bosons with a magnetic boundary interaction as introduced in Ref. 5, at the so-called "magic" points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Here we develop such a point of view by focusing on the case m=2 which corresponds to a quantum Hall bilayer. The key role of a localized impurity which couples the two layers is emphasized and the effect of noncommutativity in terms of generalized magnetic translations (GMT) is fully exploited. As a result, general GMT operators are introduced, in the form of a tensor product, which act on the QHF and defect space respectively, and a comprehensive study of their rich structure is performed.

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Time Observables in a Timeless Universe

Quantum ◽

10.22331/q-2020-10-29-354 ◽

2020 ◽

Vol 4 ◽

pp. 354

Author(s):

Tommaso Favalli ◽

Augusto Smerzi

Keyword(s):

Quantum Mechanics ◽

Energy Spectrum ◽

Hermitian Operator ◽

Dynamical Evolution ◽

Emergent Property ◽

Time Operator ◽

Static Universe ◽

Unequally Spaced ◽

Energy Ratios ◽

Time In Quantum Mechanics

Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian time operator complement of a clock Hamiltonian having an equally-spaced energy spectrum. An Hermitian operator complement of such Hamiltonian was introduced by Pegg in 1998, who named it "Age". We show here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian. We therefore show that, still following Pegg's formalism, it is possible to introduce in the PaW framework bounded clock Hamiltonians with an unequally-spaced energy spectrum with rational energy ratios. In this case time is described by a POVM and we demonstrate that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially undistinguishables.

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Resource theory of contextuality

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2019.0010 ◽

2019 ◽

Vol 377 (2157) ◽

pp. 20190010

Author(s):

Barbara Amaral

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Point Of View ◽

Resource Theory ◽

Quantum Property ◽

Theme Issue ◽

Formal Treatment ◽

Recent Developments ◽

Potential Resource

In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution, we review recent developments towards a resource theory of contextuality and connections with operational applications of this property. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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