Wave Packet Collapse Research Articles

Is Quantization a Co-Operative Phenomenon? On the Ensemble Interpretation of Quantum Physics

A fresh look at Planck's quantum, h, re-interprets action as the companion of power in a dynamic interplay of energies in a multi particle system of the micro world. An exchange of energy, δE, requires a characteristic duration, δτ, with δE and δτ tied together in a natural way. Action, the product δEδτ, must have a nonzero lower limit, h, as a classical necessity everywhere in physics. Zero h would constitute a singularity. The veritable quantum is action, not energy. Black body radiation formulas (Wien, Planck, and Rayleigh) all require this non zero h. Planck's thermodynamic approach was not consistently developed further. Einstein in his 1905 description of the photo effect chose the single "quantum of light" as statistically independent actor in radiation. The resulting discussions about the wave-particle dualism, the meaning of uncertainty, the collapse of wave packets when observed, self-interference, and related problems can be avoided by the consistent view of the ensemble interpretation. In agreement with action defined as δEδτ only co-operative phenomena produce the effects we observe. In particular, this concerns the photon, directly associated with h, as naturally interactive quantum. Careful experiments on low intensity interference suggest to take the photon out of the isolation, thus changing the general view of quantum physics with surprising consequences. Do photons transport energy or action? To understand where 20th century physics has gone a glance at the historical background is in order.

Nonlinear electrostatic ion cyclotron wave collapse and formation of wave packets in the presence of trapped electrons.

The weakly nonlinear and dispersive electrostatic ion cyclotron wave dynamics in the presence of Schamel distributed trapped electrons is studied in collisionless plasmas. The dynamics of the nonlinear wave is shown to be governed by a Schamel-Ostrovsky type equation. Analytical and numerical solutions of this equationreveal the collapse of a solitary (localized) pulse at a critical time that depends on the trapping parameter and the strength of the magnetic field. The time-dependent computational result is noteworthy, which predictstheformation of wave packets (wave group) beyond the critical time. The results are in good agreement with the astrophysical observations in auroral plasmas.

Coupled Oscillator Dynamics in Brain EEG Signals: Manifestation of synchronization and Across Frequency Energy Exchange by Neutral Turbulence

Phenomenological models, involving coupled oscillators of both deterministic and stochastic nature, have been invoked to describe the behavior of the EEG signals, with experimental validation. These models derive justification from the fact that the basic electronic unit for potential generation, incorporating capacitive, inductive, and resistive components, as well as the source, is modelled as damped driven oscillator, which can behave independently and may also exhibit synchronized dynamics with others, that can manifest in spatially correlated behavior observed in brain dynamics. Here, using a phase-space approach, we show clear evidence of oscillator dynamics to wave packet collapse and revival in the brain EEG signals, with distinct differences in healthy individuals and epileptic patients. The low frequency components exhibit single oscillator type behavior in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bistability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behavior. Wave behavior with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits that appear at 8-14Hz, centered at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.

Challenging cosmic censorship in Einstein-Maxwell-scalar theory with numerically simulated gedanken experiments

We perform extensive nonlinear numerical simulations of the spherical collapse of (charged) wavepackets onto a charged black hole within Einstein-Maxwell theory and in Einstein-Maxwell-scalar theory featuring nonminimal couplings and a spontaneous scalarization mechanism. We confirm that black holes in full-fledged Einstein-Maxwell theory cannot be overcharged past extremality and no naked singularities form, in agreement with the cosmic censorship conjecture. We show that naked singularities do not form even in Einstein-Maxwell-scalar theory, although it is possible to form scalarized black holes with charge above the Reissner-Nordstr\"om bound. We argue that charge and mass extraction due to superradiance at fully nonlinear level is crucial to bound the charge-to-mass ratio of the final black hole below extremality. We also discuss some "descalarization" mechanisms for scalarized black holes induced either by superradiance or by absorption of an opposite-charged wavepacket; in all cases the final state after descalarization is a subextremal Reissner-Nordstr\"om black hole.

Time, Equilibrium, and General Relativity

Considered is "time as an interval” including time from the past and from the future, in contrast to time as a moment. Equilibrium as the basis for a description of changing properties in physics is understood to depend on the "mean velocity theorem”, while a "time” of equilibrium resembles a center of weight. This turns out to be a good method to derive properties for any function of time t including space coordinates q(t) and expressions for the time dependent Hamiltonian. Introduced are derivatives depending on time intervals instead of time moments and with these a new relation between the Lagrangian L and the Hamiltonian H. As an application introduced is a step by step method to integrate stationary state "local” time interval measurements to beyond "locality” in General Relativity. Because of limits on the resulting time interval measures, this allows for a probabilistic interpretation for quantities that have these intervals as time domain. Thus, these measures are interesting in both a GR as a QM sense. Another application of time interval is the discussion of the measurement of starlight radiation energy and QM wave packet collapse as an example of a time dependent Hamiltonian. Finally, a relation between starlight frequency, metric and space- and time intervals is discussed. The time intervals also question the time reversal symmetry of GR.

Detection of Electronic Coherence via Two-Dimensional Electronic Spectroscopy in Condensed Phase

Two dimensional Fourier transform electronic spectroscopy (2DES) in the visible region enables direct observation of complex dynamics of molecules including quantum coherence in the condensed phase. This review aims to provide a bridge between the principles and intuitive physical description of 2DES for tutorial purpose. Special emphasis is laid upon how 2DES circumvents the restrictions from both uncertainty principle and the wave-packet collapse during the coherent detection, leading to the successful detection of the coherence in terms of energy difference between the eigenstates showing as the quantum beats; then upon the possible mixing among the pure electronic transition, single-mode and multi-mode coupled vibronic transition leading to the observed beating phenomena. Finally, recent advances in experimentally distinguishing between the electronic coherence and the vibrational coherence are briefly discussed.

Optical realization of the dissipative quantum oscillator.

An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator and enables the visualization of the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.

Wave-Packet Collapse Based on Weak Repeatability or Covariant Condition**Supported by National Natural Science Foundation of China under Grant Nos. 11461045, 11326099, 11361042, 11265010, and Natural Science Foundation of Jiangxi Province of China under Grant Nos. 20142BAB211016, 20132BAB201001, 20132BAB212009

The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.

Information transfer in generalized probabilistic theories

The tension between unitarity and wave-packet collapse is an annoying problem in quantum mechanics, while a breakthrough was made by Zurek recently from the point of view of information transfer. In this paper, we reconsider Zurek's derivation in the setting of generalized probabilistic theories (GPT), and establish that actionable information about a system can be repeatedly passed on to other systems only when the chosen states of the system have mutual zero fidelity. This may be interpreted as an extension of Zurek's result to GPT.

Wave packet construction in three-dimensional quantum billiards: Visualizing the closed orbit, collapse and revival of wave packets in the cubical billiard

We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (n x , n y , n z ) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various closed orbits. The closed orbits are possible for certain specific values of quantum numbers (n x , n y , n z ) and initial momenta (k x , k y , k z ). We observe that a cubical billiard exhibits degenerate energy levels and the path lengths of the closed orbits for these degenerate energy levels are identical. In spite of the identical path lengths, the shapes of the closed orbits for degenerate levels are different and depend upon angles 𝜃 and ϕ which we term as the sweep and the elevation angles, respectively. These degenerate levels owe their origin to the symmetries prevailing in the cubical billiard and these levels disappear completely or partially for a parallelepiped billiard as the symmetry breaks due to commensurate or incommensurate ratio of sides.

Macroscopic quantum effects for classical light

Macroscopic quantum optical effects (Schrodinger cat states, squeezing, collapse and revival) for light beams propagating in an inhomogeneous linear medium are demonstrated using exact analytical solutions of wave equation. It is shown that the coherent superposition of macroscopically distinguishable states is generated via mode interference from an initial off-axis single wave-packet. Squeezed cat states with a fidelity > 99% arise periodically and disappear rapidly within limited intervals of a propagation distance. Collapse and revival of wave packets at long-term non-paraxial evolution due to mode interference is demonstrated. Oscillations of the beam trajectory with extremely small amplitude of the order of 10-19 m which is typical of the estimated displacement caused by cosmic gravitational waves in gravity-wave detectors occur.

Constraints on the Formation and Structure of Langmuir Eigenmodes in the Solar Wind

Localized Langmuir waves are commonly observed in space plasmas and are a potential source of radio waves. Using electric field data from STEREO, it is shown that these localized Langmuir waves are eigenmodes of density wells estimated independently. An analytic model is developed for the eigenmode frequencies. The inferred depths and widths of the density wells typically only allow the zeroth-order Langmuir eigenmode to form, explaining the preponderance of single-peaked waveforms. More complicated waveforms are shown to be consistent with single eigenmode solutions of more complicated density profiles. The inferred depth of the density well increases with Langmuir wave intensity, consistent with the ponderomotive force but not wave packet collapse.

Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information

An unknown quantum state of a single system cannot be discovered, as a measured system is reprepared---it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of a macroscopic, open system (such as an apparatus), and we allow its microscopic state to change when, e.g., measured by an observer, provided that its salient features remain unchanged and that observers regard macroscopic state of the pointer as representing the same record. We conclude that repeatably accessible states of macroscopic systems (such as the states of the apparatus pointer) must correspond to orthogonal subspaces in the Hilbert space. The symmetry breaking we exhibit defies the egalitarian quantum superposition principle and unitary symmetry of the Hilbert space, as it singles out preferred subspaces. We conclude that the resulting discreteness (which underlies quantum jumps) emerges from the continuity of the core quantum postulates plus repeatability also in macroscopic and open---but ultimately quantum---systems such as measuring devices accessed by observers, where (in contrast with pure states of microsystems) repeatability is paramount.

Measurement interpretation and information measures in general probabilistic theory

Abstract The incompatibility of dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has recently been solved by Zurek from an information transfer perspective. Luo gave his derivation by relaxing the repeatability postulate. In this paper, we reconsider Luo’s derivation in the setting of general probabilistic theory (GPT). We also introduce the concept of sub- and super-fidelity in GPT and discuss their properties.

Mesoscopic states in graphene in a magnetic field: Collapse and revival of wave packets

The effects of collapse and revival of wave packets in monolayer and bilayer graphene in the presence of an external perpendicular magnetic field are investigated. An evolution of the electron wave packets, which are a superposition of states with quantum numbers n near the Landau level n0, are studied. The probability density and the average velocity of the center of packets were calculated analytically and visualized. The initial wave packet, which includes only states with positive energy, loses spatial localization, and splits into several sub-packets at the moments t = (m/n)TR, where TR is the revival time, m and n are co-primes. In addition, it is shown that a behavior of the wave packet, which consists of states of two energy bands (with En > 0 and En < 0) is more complex. Such a packet splits into two parts, which rotate with a cyclotron frequency in opposite directions. The nature of electromagnetic radiation of wave packets, undergoing periodic collapse and revival is discussed.

Do Langmuir wave packets in the solar wind collapse?

Intense localized Langmuir waves in the solar wind are often associated with type III solar radio bursts. Wave packets with a Gaussian fall‐off of electric field with distance are shown to be consistent with strong turbulence simulations. The collapse threshold for these Gaussian wave packets is calculated analytically and shown to be consistent with previous estimates and simulations. We then assess whether intense Langmuir events detected by the SWAVES instrument on the twin STEREO spacecraft during type III bursts are consistent with known conditions for wave packet collapse. Eight different type III events are selected and a total of 167 wave packets analyzed. An approximate analysis of the observed spatial scales and electric fields shows that none of the wave packets are consistent with collapse. The electric field structures predicted for collapsing wave packets, based on the nucleation mechanism and extensive three‐dimensional electrostatic and electromagnetic Zakharov simulations, are also fitted to the observed data: about a third of the packets are well fitted by a potential with a Gaussian radial function. Where good fits can be found, the wave packets do not meet the requirements for collapse. Good eigenmode fits are found for wave packets with waveforms well fitted by the structural form of collapsing wave packets. This is because the electric field envelopes of collapsing wave packets and trapped Langmuir eigenmodes are both Hermite‐Gauss functions. This rules out the possibility of wave packet collapse and strong turbulence being important processes in type III source regions.

Irreversible behaviour and collapse of wave packets in a quantum system with point interactions

A system of a particle and a harmonic oscillator, which have pure point spectra if uncoupled, is known to acquire an absolutely continuous spectrum when they are coupled by a sufficiently strong point interaction. Here, the dynamical mechanism underlying this spectral phenomenon is exposed. The energy of the oscillator is proven to exponentially diverge in time, while the spatial probability distribution of the particle collapses into a δ-function at the interaction point. On account of this result, a generalized model with many oscillators which interact with the particle at different points is argued to provide a formal model for the approximate measurement of position and collapse of wave packets.

Three-dimensional electromagnetic strong turbulence. II. Wave packet collapse and structure of wave packets during strong turbulence

Large-scale simulations of wave packet collapse are performed by numerically solving the three-dimensional (3D) electromagnetic Zakharov equations, focusing on individual wave packet collapses and on wave packets that form in continuously driven strong turbulence. The collapse threshold is shown to decrease as the electron thermal speed νe/c increases and as the temperature ratio Ti/Te of ions to electrons decreases. Energy lost during wave packet collapse and dissipation is shown to depend on νe/c. The dynamics of density perturbations after collapse are studied in 3D electromagnetic strong turbulence for a range of Ti/Te. The structures of the Langmuir, transverse, and total electric field components of wave packets during strong turbulence are investigated over a range of νe/c. For νe/c≲0.17, strong turbulence is approximately electrostatic and wave packets have very similar structure to purely electrostatic wave packets. For νe/c≳0.17, transverse modes become trapped in density wells and contribute significantly to the structure of the total electric field. At all νe/c, the Langmuir energy density contours of wave packets are predominantly oblate (pancake shaped). The transverse energy density contours of wave packets are predominantly prolate (sausage shaped), with the major axis being perpendicular to the major axes of the Langmuir component. This results in the wave packet becoming more nearly spherical as νe/c increases, and in turn generates more spherical density wells during collapse. The results obtained are compared with previous 3D electrostatic results and 2D electromagnetic results.

Three-dimensional electromagnetic strong turbulence. I. Scalings, spectra, and field statistics

The first fully three-dimensional (3D) simulations of large-scale electromagnetic strong turbulence (EMST) are performed by numerically solving the electromagnetic Zakharov equations for electron thermal speeds νe with νe/c≥0.025. The results of these simulations are presented, focusing on scaling behavior, energy density spectra, and field statistics of the Langmuir (longitudinal) and transverse components of the electric fields during steady-state strong turbulence, where multiple wave packets collapse simultaneously and the system is approximately statistically steady in time. It is shown that for νe/c≳0.17 strong turbulence is approximately electrostatic and can be explained using the electrostatic two-component model. For ve/c≳0.17 the power-law behaviors of the scalings, spectra, and field statistics differ from the electrostatic predictions and results because νe/c is sufficiently high to allow transverse modes to become trapped in density wells. The results are compared with those of past 3D electrostatic strong turbulence (ESST) simulations and 2D EMST simulations. For number density perturbations, the scaling behavior, spectra, and field statistics are shown to be only weakly dependent on νe/c, whereas the Langmuir and transverse scalings, spectra, and field statistics are shown to be strongly dependent on νe/c. Three-dimensional EMST is shown to have features in common with 2D EMST, such as a two-component structure and trapping of transverse modes which are dependent on νe/c.

From quantum no-cloning to wave-packet collapse

One aspect of the longstanding “mystery and weirdness” of wave-packet collapse in quantum mechanics has recently been dissolved by Zurek from an information transfer perspective (Phys. Rev. A 76 (2007) 052110). This result is a significant extension of the original quantum no-cloning theorem (Nature 299 (1982) 802). In this Letter we provide two closely related, but alternative, informational approaches to the orthogonality in wave-packet collapse: The first justifies and refines Zurek's derivation by relaxing the repeatability postulate to a more intuitive and simple one, the second replaces the repeatability postulate by a covariant condition of measuring apparatus. Our derivations illuminate the informational nature of wave-packet collapse.