Kryukov, Alexey (2000) Mathematics of the classical and the quantum. J. Math. Phys., 61, 082101.

Kryukov, Alexey (2000) Physics in the space of quantum states. [Preprint]

Authors: Y. Iwashita, M.Mizumoto, T. Igaki, H. Okamoto, R.A. Jameson

A memorial to Prof. Hidekuni Hidekoshi, Kyoto University, Japan – an accelerator pioneer in Japan, teacher, mentor, friend, unassuming but knowing his accomplishments and worth, frugal but generous, enjoying life. Japanese contributions given in Japanese and English, English in English.

Authors: Philip K. Schwartz, Domenico Giulini

This paper deals with the Newton–Wigner position observable for Poincar\’e-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton–Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton–Wigner position as `centre of spin’, already proposed by Fleming in 1965 again in the quantum context.

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed $k$. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when $k$ is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.

Everett’s relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett’s own one in the Schr\”odinger picture, makes manifest the locality of Everettian multiplicity, and its inherently approximative nature, and its origin in certain kinds of entanglement and locally inaccessible information. Our construction also allows us to give a more precise definition of an Everett ‘universe’ (which is fully quantum, not quasi-classical), and we compare the Everettian decomposition of a quantum state with the foliation of a spacetime.

The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three important associated 1 dimensional problems were solved: the free particle case, the infinite potential well, and the harmonic potential. The wave equations generated reproduced the same type of 2-order ODE observed in classical dissipative systems, and produced quantized energy levels. In the infinite potential well, a zero-point energy emerges, which can be fitted to the rest energy of the particle described by special relativity, given by relationship $E_r=mc^2$. In the harmonic potential, new fractional creation and destruction operators were introduced to solve the problem in the energy basis. The energy eigenvalues found are different to the ones reported by earlier approaches to the quantum damped oscillator problem reported by other authors. In this case, a direct relationship between the relativistic rest energy of the particle and the expected value of the fractionary kinetic energy in the base state was obtained. We conclude that there exists a relationship between fractional kinetic energy and special relativity energies, that remains unclear and needs further exploration, but also conclude that the current form of transforming fractionary momentum operators to the position basis will yield non-observable imaginary momentum quantities, and thus a correction to the way of transforming them needs to be explored further.

Publication date: Available online 6 August 2020

Source: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Author(s): Michael Friedman

Authors: Yasaman K. Yazdi, Marco Letizia, Achim Kempf

We study discrete Lorentzian spectral geometry by investigating to what extent causal sets can be identified through a set of geometric invariants such as spectra. We build on previous work where it was shown that the spectra of certain operators derived from the causal matrix possess considerable but not complete power to distinguish causal sets. We find two especially successful methods for classifying causal sets and we computationally test them for all causal sets of up to $9$ elements. One of the spectral geometric methods that we study involves holding a given causal set fixed and collecting a growing set of its geometric invariants such as spectra (including the spectra of the commutator of certain operators). The second method involves obtaining a limited set of geometric invariants for a given causal set while also collecting these geometric invariants for small `perturbations’ of the causal set, a novel method that may also be useful in other areas of spectral geometry. We show that with a suitably chosen set of geometric invariants, this new method fully resolves the causal sets we considered. Concretely, we consider for this purpose perturbations of the original causal set that are formed by adding one element and a link. We discuss potential applications to the path integral in quantum gravity.

Authors: Ram Brustein, Yotam Sherf

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical blackholes (BHs). Here we show, using standard time-independent quantum perturbation theory, that for a quantum BH, generically, the Love numbers are nonvanishing and negative, and that their magnitude depends on the lowest lying levels of the quantum spectrum of the BH. We calculate the quadrupolar electric quantum Love number of nonrotating BHs and show that it depends most strongly on the first excited level of the quantum BH. We then compare our results to the same Love number of exotic ultra compact objects and to that of classical compact stars and highlight their different parametric dependence. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favourable circumstances, its magnitude is large enough to imprint an observable signature on the gravitational waves emitted during the inspiral phase of two moderately spinning BHs.

Author(s): Mirjam Weilenmann and Roger Colbeck

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements. In other words it is concerned with the question of whether we can te…

[Phys. Rev. Lett. 125, 060406] Published Thu Aug 06, 2020

Hermens, Ronnie (2020) Completely real? A critical note on the claims by Colbeck and Renner. [Preprint]

Nature Physics, Published online: 04 August 2020; doi:10.1038/s41567-020-1013-7

Test your theory

Nature Physics, Published online: 04 August 2020; doi:10.1038/s41567-020-1010-x

The persistent under-representation of Black physicists is a systemic problem that requires will, money and long-term commitment to be solved.

Nature Physics, Published online: 04 August 2020; doi:10.1038/s41567-020-1001-y

The unifying role of topology

Ciepielewski, Gerardo Sanjuan and Okon, Elias and Sudarsky, Daniel (2020) On Superdeterministic Rejections of Settings Independence. [Preprint]

Lopez, Cristian (2019) PhD Thesis:The Arrow of Time and Time Symmetry in non-Relativistic Quantum Mechanics. [Preprint]

Chen, Eddy Keming (2020) The Past Hypothesis and the Nature of Physical Laws. [Preprint]

de Ronde, Christian (2020) Quantum Theory Needs No ‘Interpretation’ But ‘Theoretical Formal-Conceptual Unity’ (Or: Escaping Adán Cabello’s “Map of Madness” With the Help of David Deutsch’s Explanations). [Preprint]

Norton, John D. (2015) You are not a Boltzmann brain. [Preprint]

Lopez, Cristian (2020) Time’s Direction and Orthodox Quantum Mechanics: Time Symmetry and Measurement. [Preprint]

López, Cristian (2020) Time Symmetry in Three Dimensions. [Preprint]

Lopez, Cristian (2020) The Physics and the Philosophy of Time Reversal in Standard Quantum Mechanics. [Preprint]