Electron Decoherence at Zero Temperature

In this study, we show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. We do not delve into a deep discussion regarding what the measurement problem actually is, and only examine the problems that seem to exist between classical and quantum physics. Relations between quantum and classical equations of motion are briefly reviewed to show that the transition from a superposition of quantum states to an eigenstate, namely, decoherence, is necessary to ensure that the expectation values in quantum mechanics obey the classical equations of motion. Several Bell-type inequalities and the Kochen-Specker theorem are also reviewed to clarify the concepts of nonseparability and counterfactual definiteness in quantum mechanics. The main objective of this study is to show that decoherence is an inherent characteristic of quantum states caused by the quantum uncertainty relation. We conclude that the quantum measurement process can indeed be explained within the framework of pure quantum mechanics. We also show that our conclusion is consistent with the counterfactual indefiniteness of quantum mechanics.

We have made the first demonstration that low error rate quantum cryptography over long distances (14km) of installed optical fiber in a real-world environment, subject to uncontrolled temperature and mechanical influences, representing an important new step towards incorporation of quantum cryptography into existing information security systems. We also point out that the high visibility single-photon interference in our experiment allows us to infer a test of the superposition principle of quantum mechanics: a photon reaching the detector has traveled over 14km of optical fiber in a wavepacket comprising a coherent superposition of two components that are spatially separated by about 2m. In principle, there are decoherence processes (or even possible modifications of quantum mechanics) that could cause the photon`s wavefunction to collapse into one component or the other during propagation, leading to a reduction in visibility. However, our results are consistent with no such loss of quantum coherence during the 67-{mu}s propagation time.

We find that in supersymmetric theories gravitodynamic effects scaled by the inverse of the Planck mass can induce baryon decay at an observable rate. In a minimal supersymmetric (susy) grand unified theory (GUT) the dominant gravitationally induced baryon decay mode is B→ν̄+K, with a likely admixture of p→(e+or μ+)+K. As a by‐product, we present an improved estimate of Higgs‐mediated baryon decay branching ratios in minimal susy GUTs. We consider the possibility that a loss of quantum coherence may be observable in gravitationally induced baryon decay, but argue that this would be difficult to reconcile with successful experimental tests of quantum mechanics.

Baby universes and the non-renormalizability of gravity

Rotational tunnelling and librational excitations: The loss of quantum coherence

The classical concept of molecular structure (namely, a set of atoms with a well‐defined geometrical arrangement in space) originated well before the advent of quantum theory, and, contrary to widespread views, these two conceptual schemes (classical molecular structure and quantum theory) are not easy to reconcile. We begin with a preliminary discussion of molecular structure in terms of space and time correlations in the framework of quantum theory. Then we summarize the salient features of some critical views raised‐during recent years (essentially by Woolley) concerning the concept of molecular structure. The essential claim of this viewpoint is that “molecular structure” is not an intrinsic attribute of an isolated molecule, and appears rather as an effect of the environment (other molecules? vacuum electromagnetic field, according to quantum electrodynamics?). Afterwards, we discuss these issues in detail: we show that it is necessary to distinguish between a “quantum” or “potential” structure (which may be deduced in a straightforward way from the quantum treatment of the molecule), and the “classical” molecular structure (according to which the molecule is considered as a set of rotating and vibrating material points, corresponding to the atoms); we briefly discuss some aspects of the Born–Oppenheimer approximation. From our discussion, we deduce that the “classical structure” concept is indeed non‐trivial from a purely quantum‐mechanical point of view; in actual fact, it is related to the problem of the “classical limit” of quantum mechanics, and it appears that, at the present time, none of these classical concepts and behaviours is convincingly derivable from a strict quantum mechanical basis. Finally, we consider these same problems from the point of view of stochastic electrodynamics (SED), which is one of the stochastic models for microphysics proposed so far as a possible alternative or extension of usual quantum theory. In the framework of such a theory, the “classical limit” and, in particular, the “classical molecular structure” no longer poses a problem, but aside from these satisfactory qualitative aspects, several quantitative failures of SED prevent us from accepting it, at least in its present state, as a genuine physical alternative to quantum theory. We therefore conclude that “classical molecular structure”, and classical concepts in general, remain an open problem in the framework of present‐day quantum physics.

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

We show that the Atiyah–Singer index theorem of Dirac operator can be directly proved in the canonical formulation of quantum mechanics, without using the path-integral technique. This proof takes advantage of an algebraic isomorphism between Clifford algebra and exterior algebra in small τ (high temperature) limit, together with simple properties of quantum harmonic oscillator. Compared to the proofs given by full symbol calculus and heat kernel, we try to prove this theorem in a more quantum mechanical way.

From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the ‘quantum Cheshire Cat’: if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat’s nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.

ABSTRACTWe herein explain the phase of ferroelectrics by reference to finite block spin theory, in which the phase of ferroelectrics may be considered as being a ferroelectric ordering between pseudo block spins comprised of random pseudo spins, that is, dipoles that have a majority of individual spins in a given sense. By making use of the Curie-Weiss law of pseudo block spins for ferroelectrics, we obtained the susceptibility for the lower and higher temperature approximations of the Brillouin function. According to our viewpoint, the state of dipole glass can be regarded as paraelectric ordering of pseudo block spins with higher temperature limit and lower temperature limit of the Brillouin function. For Rochelle salts, this phase may have ferroelectric and dipole glass mixed states where higher temperature limit and lower temperature limit and in the intermediate range between these a ferroelectric state happens.

In this and the next chapter, we begin a study of the behavior of the spectrum of Schrodinger operators in the semiclassical regime. There is much literature on these topics, and we provide an outline in the Notes to this chapter. The material here follows a part of the work of Simon [Sim5]. In quantum mechanics, the Laplacian plays the role of the energy of a free particle. But, the Laplacian apparently has the dimensions of (length)-2. This is because in our discussions of the Schrodinger operator, we have chosen to work in simple units in which the mass m = 1/2 and Planck’s constant h is taken to be 2π. In these units, the coefficient of the kinetic energy H 0 = -△ is 1. If we restore these constants, the actual differential operator in quantum mechanics representing the energy of a free particle is. The Planck constant h is approximately 6.624 x 10-27 ergs/sec. This is very small except on atomic scales. That is, the length scales over which quantum effects are important depend on h (for example, the Compton wavelength of an electron or the Bohr radius of an atom). This observation provides us with one way to understand the transition from classical to quantum phenomena. We consider quantum theory in which Planck’s constant has been replaced by a small parameter. We then try to understand quantum mechanics in terms of the classical theory obtained as the limit of this quantum theory as the parameter is taken to zero. We call this limit h = 0 the classical limit since all quantum effects have been suppressed. The regime in which this parameter is nonzero, but taken arbitrarily small, is called the semiclassical regime. In this regime, the behavior of the quantum mechanical system should be dominated by the limiting h = 0 classical system.

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in terms of phase-space distributions. Finite dimensional systems have historically been an issue. In recent works [Phys. Rev. Lett. 117, 180401 and Phys. Rev. A 96, 022117] we presented a framework for representing any quantum state as a complete continuous Wigner function. Here we extend this work to its partner function -- the Weyl function. In doing so we complete the phase-space formulation of quantum mechanics -- extending work by Wigner, Weyl, Moyal, and others to any quantum system. This work is structured in three parts. Firstly we provide a brief modernized discussion of the general framework of phase-space quantum mechanics. We extend previous work and show how this leads to a framework that can describe any system in phase space -- putting it for the first time on a truly equal footing to Schr\"odinger's and Heisenberg's formulation of quantum mechanics. Importantly, we do this in a way that respects the unifying principles of "parity" and "displacement" in a natural broadening of previously developed phase space concepts and methods. Secondly we consider how this framework is realized for different quantum systems; in particular we consider the proper construction of Weyl functions for some example finite dimensional systems. Finally we relate the Wigner and Weyl distributions to statistical properties of any quantum system or set of systems.

We investigate quantum gravity corrections due to the generalized uncertainty principle on three-dimensional weakly interacting Bose gases at both zero and finite temperatures using the time-dependent Hatree–Fock–Bogoliubov theory. We derive useful formulas for the depletion, the anomalous density, and some thermodynamic quantities such as the chemical potential, the ground-state energy, the free energy, and the superfluid density. It is found that the presence of a minimal length leads to modify the fluctuations of the condensate and its thermodynamic properties in the weak and strong quantum gravitational regimes. Unexpectedly, the interplay of quantum gravity effects and quantum fluctuations stemming from interactions may lift both the condensate and the superfluid fractions. We show that quantum gravity minimizes the interaction force between bosons leading to the formation of ultradilute Bose condensates. Our results which can be readily probed in current experiments may offer a new attractive possibility to understand gravity in the framework of quantum mechanics.

Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has beenextended, first to quantum field theories, gauge field theories, and noweven string theory. It is used every day by thousands of physicists tocalculate physical phenomena to exquisite precision, with no ambiguity inthe results. To claim that this is a theory which is not understood bythose physicists is absurd. And yet, as eminent a physicist as RichardFeynman, who did as much as anyone else to extend quantum theory to field theories and was a master at producing those exquisite calculations, could say that anyone who claimed they understood quantum theory clearly did not understand quantumtheory.One hundred years ago Einstein postulated one of the most unsettlingfeatures of the theory, the wave-particle duality, with his particulateexplanation for light of the photoelectric effect, and an explanation whichwas in direct conflict with Maxwell's brilliant development of a wave, orfield, theory of light. Einstein believed that the particulate nature would ultimately be explainable by some sort of non-linear theory of electromagnetism, and was outraged by the acceptance of the community of the probabilistic quantum theory. His programme was of course dealt a (near?) fatal blow by Bell's discovery that the three desiderata - a theory which agrees with experiment, a theorywhich is local in its effects, and a theory in which nature, at its heart, isnot probabilistic - are incompatible.That discomfort felt by Einstein and by Feynman is felt by numerous otherpeople as well. This discomfort is heightened by the fact that the theoryof gravity, another of Einstein's great achievements, has resisted allefforts at reconciliation with quantum mechanics. This book explores thatdiscomfort, and tries to pin down what the locus of that discomfort is.For many, the locus is in the probabilistic nature at the heart of thetheory. Nature should surely, at some fundamental level, know what it isdoing. The photon, despite our inability to measure it, should know whereit is and how fast it is going. The papers by t'Hooft, Hiley, and Smolin fall intothis camp. Some suspect that the macroscopic world of our immediate senseexperiences, and the microscopic world of quantum phenomena, are genuinelydifferent, that the fundamental conceptual nature of physics changes fromone to the other, with some unknown boundary between them. Penrose, in hispreface alludes to his speculations on this, as does Leggett to his ownspeculations in his paper. And a number of articles (e.g., by Hartle, Rovelli, and others) opine that if only everyone looked at quantum mechanics in the right way (their way), it would lose its mystery, and be as natural as Newton's world view. (I myself tend to this position, which is however somewhat tempered by the realization that the clarity and naturalness of my viewpoint is not shared by the others who believe equally firmly in their own natural, clear, but radicallydifferent, viewpoint). A number of articles simply examine thecounterintuitive nature of quantum theory in general, using it to makesense of time travel (Greenberger and Svozil) and demonstrating the unusualfeatures of induction about the past from present observations withinquantum theory (Aharonov and Dolev).The book is not free from rather overblown titles (e.g., 'Liberation andPurification from Classical Prejudice', or 'A Quantum Theory of the HumanPerson') but those articles nevertheless contain at least amusing speculations.In quantum gravity, the incompatibilities between the two masterstrokes of thetwentieth century are highlighted. There is a strong suspicion amongstmany in this field that progress in understanding quantum gravity demands a deeper understanding of the great mystery of quantum theory which this book explores. This book is a useful and, at times, fascinating introduction to the flounderings which are taking place in trying to understand not only the solution but even what the problem is. Finally, however, the question of the title of this book remains unanswered.

Pushed to the limit: consequences of climate change for the Araucariaceae: a relictual rain forest family.