# Weekly Papers on Quantum Foundations (4)

Extractable work in quantum electromechanics. (arXiv:2201.07819v1 [quant-ph])

Recent experiments have demonstrated the generation of coherent mechanical oscillations in a suspended carbon nanotube, which are driven by an electric current through the device above a certain voltage threshold, in close analogy with a lasing transition. We investigate this phenomenon from the perspective of work extraction, by modelling a nano-electromechanical device as a quantum flywheel or battery that converts electrical power into stored mechanical energy. We introduce a microscopic model that qualitatively matches the experimental finding, and compute the Wigner function of the quantum vibrational mode in its non-equilibrium steady-state. We characterise the threshold for self-sustained oscillations using two approaches to quantifying work deposition in non-equilibrium quantum thermodynamics: the ergotropy and the non-equilibrium free energy. We find that ergotropy serves as an order parameter for the phonon lasing transition. The framework we employ to describe work extraction is general and widely transferable to other mesoscopic quantum devices.

Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics. (arXiv:2201.07919v1 [hep-th])

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this Letter, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis’ probability amplitudes, whose non-extensivity parameter $q$ monotonically increases with the GUP deformation parameter $\beta$. Secondly, for $\beta < 0$ (i.e., $q < 1$), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi-classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasi-classical regime has relevant observational consequences. We discuss some of the implications.

Generation of vortex particles via weak measurements. (arXiv:2201.07997v1 [hep-ph])

While twisted photons with orbital angular momentum can be generated in several ways, their massive counterparts — vortex electrons, neutrons, or atoms — can be obtained so far only via diffraction techniques, not applicable for relativistic energies. Here we show that particles with phase vortices, including hadrons, ions, and nuclei, can be generated during emission in helical undulators, via Cherenkov radiation, in collisions with intense laser beams, in such scattering and annihilation processes as $e\mu \to e\mu, ep \to ep$, etc. We elucidate that the key element in obtaining them is not the process itself but the post-selection protocol due to quantum entanglement. A final particle acquires a phase vortex if the other final particle’s momentum is weakly measured with no post-selection of its azimuthal angle. This technique can be used for generating all types of vortex particles, it can be adapted for ultrarelativistic beams of modern colliders for hadronic and spin studies, and it can also facilitate the development of sources of hard X-ray and $\gamma$-range twisted photons.

On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook. (arXiv:2104.10151v3 [quant-ph] UPDATED)

Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\”odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s). Integrating developments are: a) entanglement of a microscopic system with its classical environment accords it a time evolution description, the time dependent Schr\”odinger equation, where t is the laboratory time measured by clocks; b) canonical quantization of Special Relativity yields both the Dirac Hamiltonian and a self adjoint “time” operator, restoring to position and time the equivalent footing accorded to energy and momentum in Relativistic Quantum Mechanics. It introduces an intrinsic time property {\tau} associated with the mass of the system, and a basis additional to the usual configuration, momentum and energy basis. As a generator of momentum displacements and consequently of energy, it invalidates Pauli’s objection to the existence of a time operator. It furthermore complies with the requirements to condition the other observables in the conditional interpretation of QG. As Pauli’s objection figures explicit or implicitly in most current developments of QM and QG, its invalidation opens to research the effect of this new two times perspective on such developments.

Anomalous weak values are caused by disturbance. (arXiv:2108.04733v3 [quant-ph] UPDATED)

In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin of an electron (along some axis) to be 100. We argue that the disturbance caused by the weak measurement, while small, is sufficient to significantly affect the measurement result, and that this is the most reasonable explanation of anomalous weak values.

On Circular Orbits in Einstein’s Theory of Gravitation. (arXiv:2201.07971v1 [physics.hist-ph])

Authors: S.A. Kaplan

The preprint is an English translation of the paper by famous astrophysicist Samuil Kaplan (1921-1978) “O krugovykh orbitakh v teorii tyagoteniya Einsteina (On circular orbits in Einstein’s theory of gravitation)”, published in 1949 in the Journal of Experimental and Theoretical Physics (Vol. 19, No. 10, pp. 951-952) in Russian. This important 1 and 1/3 page paper is still inaccessible to a wide range of experts and students due to the lack of such translation. This paper is the first scientific publication of Samuil Kaplan and the pioneering work in this field. The aim of this presentation is to make the article available to a wide range of experts in the field of general relativity, relativistic astrophysics and the history of science, as well as to honor its author on the occasion of the 100th anniversary of his birth.

Lost Horizon? — Modeling Black Holes in String Theory. (arXiv:2201.08250v1 [physics.hist-ph])

Authors: Nick HuggettKeizo Matsubara

The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these goals are obtained in string theory. We review black hole thermodynamics, and then explicate the general stringy derivation of classical spacetimes, the construction of a simple black hole solution, and the derivation of its entropy. With that in hand, we address some important philosophical and conceptual questions: the confirmatory value of the derivation, the bearing of the model on recent discussions of the so-called ‘information paradox’, and the implications of the model for the nature of space.

Quantum Gravitational Corrections to the Entropy of a Reissner-Nordstr\”om Black Hole. (arXiv:2201.08293v1 [hep-th])

Starting from an effective action for quantum gravity, we calculate the quantum gravitational corrections to the Wald entropy of a four dimensional non-extremal Reissner-Nordstr\”om (RN) black hole in the limit of small electric charge, generalising a previous calculation carried out by Calmet and Kuipers [1] for a Schwarzschild black hole. We show that, at second order in the Ricci curvature, the RN metric receives quantum corrections which shift the classical position of the event horizon. We apply the Wald entropy formula by integrating over the perimeter of the quantum corrected event horizon. We then compute the quantum gravitational corrections to the temperature and the pressure of the black hole.

On the origin of cosmic web. (arXiv:2201.06882v2 [astro-ph.CO] UPDATED)

The emergence of one and two-dimensional configurations — Zeldovich pancakes — progenitors of the observed filaments and clusters and groups of galaxies, is predicted by means of a developed kinetic approach in analyzing the evolution of initial density perturbations. The self-consistent gravitational interaction described by Vlasov-Poisson set of equations with branching conditions is shown to predict two-dimensional structures as of layers of increased density and voids between them, i.e. the cellular macro-structure of the Universe. The modified potential of weak-field General Relativity is involved, which enables one to explain the Hubble tension, revealing the conceptual discrepancy in the local galactic flows and the cosmological expansion. This demonstrates the possible essential role of self-consistent gravity in the formation of the cosmic web.

The End of Expansion. (arXiv:2201.07704v1 [astro-ph.CO] CROSS LISTED)

If dark energy is a form of quintessence driven by a scalar field $\phi$ evolving down a monotonically decreasing potential $V(\phi)$ that passes sufficiently below zero, the universe is destined to undergo a series of smooth transitions: the currently observed accelerated expansion will cease; soon thereafter, expansion will come to end altogether; and the universe will pass into a phase of slow contraction. In this paper, we consider how short the remaining period of expansion can be given current observational constraints on dark energy. We also discuss how this scenario fits naturally with cyclic cosmologies and recent conjectures about quantum gravity.

On the objectivity of measurement outcomes

Okon, Elias (2022) On the objectivity of measurement outcomes. [Preprint]

Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit

Author(s): Xiaosong Zhu, Peixiang Lu, and Manfred Lein

If the time evolution of a quantum state leads back to the initial state, a geometric phase is accumulated that is known as the Berry phase for adiabatic evolution or as the Aharonov-Anandan (AA) phase for nonadiabatic evolution. We evaluate these geometric phases using Floquet theory for systems in…

[Phys. Rev. Lett. 128, 030401] Published Thu Jan 20, 2022

Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice

Nature Physics, Published online: 20 January 2022; doi:10.1038/s41567-021-01476-w

Studies of first-order phase transitions in quantum simulators have so far been restricted to the weakly interacting regime. A tunable discontinuous phase transition has now been realized with strongly correlated atoms in a driven optical lattice.

Branch-counting in the Everett interpretation of quantum mechanics

Saunders, Simon (2021) Branch-counting in the Everett interpretation of quantum mechanics. Proceedings of the Royal Society A, 477.

All quantum mixtures are proper

Castellani, Leonardo (2022) All quantum mixtures are proper. [Preprint]