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Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond, governed by one of the conformal quantum mechanics (CQM) symmetry generators: the noncompact hyperbolic operator $S$. In this paper, we show that the unbounded nature of $S$ endows it with a quantum instability, which is a generalization of a similar property exhibited by the inverted harmonic oscillator potential. Our analysis is semiclassical, including a detailed phase-space study of the classical dynamics of $S$ and its dual operator $R$, and a general semiclassical framework yielding basic instability and thermality properties that play a crucial role in the quantum behavior of the theory. For an observer with a finite lifetime $\mathcal{T}$, the detected temperature $T_D = 2 \hbar/(\pi \mathcal{T})$ is associated with a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate., Comment: This paper has been withdrawn by the authors as it is now superseded by its merger with paper arXiv:2407.18177. The merged paper arXiv:2407.18177 is also published as: Phys. Rev. D 110, 124043 (2024); DOI: https://doi.org/10.1103/PhysRevD.110.124043

An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(\pi \mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM: (i) is the generator of the time evolution of a diamond observer; (ii) its dynamical behavior leads to the predicted thermal nature; and (iii) its associated quantum instability has a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials., Comment: 52 pages, 5 figures. This is a merger of the original version 1 with the withdrawn paper arXiv:2407.18191. The merger unifies and supersedes both papers, as in the published Phys. Rev. D article. Also, the title has been slightly expanded and typos were corrected

Entanglement degradation appears to be a generic prediction in relativistic quantum information whenever horizons restrict access to a region of spacetime. This property has been previously explored in connection with the Unruh effect, where a bipartite entangled system composed of an inertial observer (Alice) and a uniformly accelerated observer (Rob) was studied, with entanglement degradation caused by the relative acceleration -- and with equivalent results for the case when Alice is freely falling into a black hole and Rob experiences a constant proper acceleration as a stationary near-horizon observer. In this work, we show that a similar degradation also occurs in the case of an entangled system composed of an inertial observer (Alice) and a "diamond observer" (Dave) with a finite lifetime. The condition of a finite lifetime is equivalent to the restriction of Dave's access within a causal diamond. Specifically, if the system starts in a maximally entangled state, prepared from Alice's perspective, entanglement degradation is enforced by the presence of the diamond's causal horizons., Comment: 42 pages, 4 figures

A path-integral approach is used to study the spectral properties of the generators of the SO(2,1) symmetry of conformal quantum mechanics (CQM). In particular, we consider the CQM version that corresponds to the weak-coupling regime of the inverse square potential. We develop a general framework to characterize a generic symmetry generator $G$ (linear combinations of the Hamiltonian $H$, special conformal operator $K$, and dilation operator $D$), from which the path-integral propagators follow, leading to a complete spectral decomposition. This is done for the three classes of operators: elliptic, parabolic, and hyperbolic. We also highlight novel results for the hyperbolic operators, with a continuous spectrum, and their quantum-mechanical interpretation. The spectral technique developed for the eigensystem of continuous-spectrum operators can be generalized to other operator problems., Comment: Updated with published version

The thermodynamics of ``horizon brightened acceleration radiation'' (HBAR), due to a random atomic cloud freely falling into a black hole in a Boulware-like vacuum, is shown to mimic the thermodynamics of the black hole itself. The thermodynamic framework is developed in its most general form via a quantum optics master equation, including rotating (Kerr) black holes and for any set of initial conditions of the atomic cloud. The HBAR field exhibits thermal behavior at the Hawking temperature and an area-entropy-flux relation that resembles the Bekenstein-Hawking entropy. In addition, this general approach reveals:(i) the existence of an HBAR-black-hole thermodynamic correspondence that explains the HBAR area-entropy-flux relation;(ii) the origin of the field entropy from the near-horizon behavior, via conformal quantum mechanics (CQM)., Comment: 31 pages, 1 figure

A quantum-optics approach is used to study the nature of the acceleration radiation due to a random atomic cloud falling freely into a generalized Schwarzschild black hole through a Boulware vacuum. The properties of this horizon brightened acceleration radiation (HBAR) are analyzed with a master equation that is fully developed in a multimode format. A scheme for the coarse-graining average for an atomic cloud is considered, with emphasis on the random injection scenario, which is shown to generate a thermal state. The role played by conformal quantum mechanics (CQM) is shown to be critical for detailed balance via a Boltzmann factor governed by the near-horizon physics, with the unique selection of the Hawking temperature. The HBAR thermal state is the basis for a thermodynamic framework that parallels black hole thermodynamics., Comment: 34 pages, 2 figures

An atom falling freely into a Kerr black hole in a Boulware-like vacuum is shown to emit radiation with a Planck spectrum at the Hawking temperature. For a cloud of falling atoms with random initial times, the radiation is thermal. The existence of this radiation is due to the acceleration of the vacuum field modes with respect to the falling atom. Its properties can be traced to the dominant role of conformal quantum mechanics (CQM) in the neighborhood of the event horizon. We display this effect for a scalar field, though the acceleration radiation has a universal conformal behavior that is exhibited by all fields in the background of generic black holes., Comment: 21 pages, expanded sections for more detailed discussion, format changed to regular article from letter

A two-level atom freely falling towards a Schwarzschild black hole was recently shown to detect radiation in the Boulware vacuum in an insightful paper [M. O. Scully et al., Proc. Natl. Acad. Sci. U.S.A. 115, 8131 (2018)]. The two-state atom acts as a dipole detector and its interaction with the field can be modeled using a quantum optics approach. The relative acceleration between the scalar field and the detector causes the atom to detect the radiation. In this paper, we show that this acceleration radiation is driven by the near-horizon physics of the black hole. This insight reinforces the relevance of near-horizon conformal quantum mechanics for all the physics associated with the thermodynamic properties of the black hole. We additionally highlight the conformal aspects of the radiation that is given by a Planck distribution with the Hawking temperature., Comment: 23 pages, 2 figures, Accepted to be published in PRD

In contrast with the 3D result, the Beth-Uhlenbeck (BU) formula in 1D contains an extra -1/2 term. The origin of this -1/2 term is explained using a spectral density approach. To be explicit, a delta-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in 1D. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the delta-function potential, the method and result are valid for more general potentials. Additionally, the 1D Levinson's theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in 1D have a universal source: a pole at zero energy. Similar calculations using quantum field theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (appendix A)., Comment: 12 pages, 3 figures

We are exploring low-dose proton radiography and computed tomography (pCT) as techniques to improve the accuracy of proton treatment planning and to provide artifact-free images for verification and adaptive therapy at the time of treatment. Here we report on comprehensive beam test results with our prototype pCT head scanner. The detector system and data acquisition attain a sustained rate of more than a million protons individually measured per second, allowing a full CT scan to be completed in six minutes or less of beam time. In order to assess the performance of the scanner for proton radiography as well as computed tomography, we have performed numerous scans of phantoms at the Northwestern Medicine Chicago Proton Center including a custom phantom designed to assess the spatial resolution, a phantom to assess the measurement of relative stopping power, and a dosimetry phantom. Some images, performance, and dosimetry results from those phantom scans are presented together with a description of the instrument, the data acquisition system, and the calibration methods., Comment: Conference on the Application of Accelerators in Research and Industry, CAARI 2016, 30 October to 4 November 2016, Ft. Worth, TX, USA

Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force., Comment: 3 pages, no figures

A model is discussed in which an electric field induces quantum nucleation of soliton-antisoliton pairs in a pinned charge or spin density wave. Coulomb blockade prevents pair creation until the electric field exceeds a sharp threshold value, which can be much smaller than the classical depinning field. We calculate the vacuum state energy and expectation value of the phase, which is treated as a quantum scalar field. We find that the phase can also be much smaller, below threshold, than predicted by classical ``sliding'' density wave models., Comment: 9 pages, 5 figures

Chiral symmetry is consistently implemented in the two-nucleon problem at low-energy through the general effective chiral lagrangian. The potential is obtained up to a certain order in chiral perturbation theory both in momentum and coordinate space. Results of a fit to scattering phase shifts and bound state data are presented, where satisfactory agreement is found for laboratory energies up to about 100 Mev., Comment: Postscript file; figures available by request

We investigate the issue of coordinate redefinition invariance by carefully performing nonlinear transformations in the discretized quantum mechanical path integral. By resorting to hamiltonian path integral methods, we provide the first complete derivation of the extra terms (beyond the usual jacobian term) which arises in the action when a nonlinear transformation is made. We comment on possible connections with the renormalization group, by showing that these extra terms may emerge from a ``blocking" procedure. Finally, by performing field redefinitions before and after dimensional reduction of a two dimensional field theory, we derive an explicit form fo an extra term appearing in a field theory., Comment: 35pp. A more rigorous derivation of the quantum mechanical extra term is given. Work on the extension to the quantum field theory case is in progress

The equivalence between the covariant and the non-covariant version of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of Electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the coratiant and non-covariant approaches, which had not been fully clarified in the literature., Comment: 21 pages, preprint # UTTG-02-93, UB-ECM-PF 93/5. To appear in Phys. Rev. D