M. A. Doncheski, R. W. Robinett
We discuss some of the properties of the `collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and the time variation of the uncertainty principle product $Δx_t \cdot Δp_t$. We make explicit use of Gaussian-like wave packets in the analysis, but also comment on other general forms.
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We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.
Image Theory for the Single Bounce Quantum Gravimeter
本文提出单 bounce 量子重力仪的图像理论，通过连续能量基分解解释量子干涉起源，并探讨参数空间和测量精度。
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical Feynman path integral is a very appealing approach, as it approximates the propagator by a closed-form expression (a sum over a finite number of classical paths). In this paper we solve the classical path enumeration problem. We obtain closed-form expressions for the initial velocity, bounce times, focal times, action, van Vleck determinant, and Morse index for ea…
We discuss the time development of Gaussian wave packet solutions of the quantum bouncer' (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization of the expectation values and uncertainties of position and momentum variables during a single quasi-classical period as well as during the long term collapsed phase and several revivals. This approach complements existing analytic and numerical analyses of this system, as well as being useful for comparison with similar results for the harmonic oscillator an…
Phase space anatomy of dynamical quantum phase transitions
本研究通过离散相空间区分了动力学量子相变中序参量与返回率两种定义，揭示了干涉在返回奇异分支选择中的独立作用。
We identify a signature of quantum gravitational effects that survives from the early universe to the current era: Fluctuations of quantum fields as seen by comoving observers are significantly influenced by the history of the early universe. In particular we show how the existence (or not) of a quantum bounce leaves a trace in the background quantum noise that is not damped and would be non-negligible even nowadays. Furthermore, we estimate an upper bound for the typical energy and length scales where quantum effects are relevant. We discuss how this signature might be observed and therefore …
The analytical bounce solution is derived in terms of the polygamma function in the Caldeira-Leggett's dissipative quantum tunneling model. The classical action for the bounce solution lies between the upper and lower bounds in the full range of $α$, where $α$ is a dissipation coefficient. The bounce peak point increases from 1 to 4/3 with increase of $α$. In spite of various nice features we have shown that the solution we have derived is not exact one by making use of the zero mode argument in the linearized fluctuation equation. However, our solution can be a starting point for approximate …
We present a unified formulation of quantum holonomy which is capable of describing all of its known varieties. The full role of non-Abelian gauge connection is elucidated. As examples, solvable models of quantum kicked spin are analyzed. They are shown to exhibit spiral holonomy, as well as Berry phase and Wilczek-Zee holonomy.
We analyze the big bounce transition of the quantum FRW model in the setting of the nonstandard loop quantum cosmology (LQC). Elementary observables are used to quantize composite observables. The spectrum of the energy density operator is bounded and continuous. The spectrum of the volume operator is bounded from below and discrete. It has equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of spacetime at semiclassical level which may be detected in astro-cosmo observations. The nonstandard LQC method has a free parameter that should be fixed…
Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
本文建立统一框架研究非厄米系统中的动力学量子相变，揭示其几何正交性与涌现拓扑特征，为开放系统量子临界性奠定原理基础。
Single-bounce quantum gravimeter to measure the free-fall of anti-hydrogen
该研究提出了一种基于单 bounce 量子重力仪的新型装置，用于测量反氢的自由下落，通过提高测量精度验证等效原理。
The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly equivalent to the microcanonical mixed state at the same energy. We derive an expression for the time-dependent gas density which depends on the initial gas state only via a few thermodynamic parameters.…
Analyzing quantum cosmological scenarios containing one scalar field with exponential potential, we have obtained a universe model which realizes a classical dust contraction from very large scales, the initial repeller of the model, and moves to a stiff matter contraction near the singularity, which is avoided due to a quantum bounce. The universe is then launched in a stiff matter expanding phase, which then moves to a dark energy era, finally returning to the dust expanding phase, the final attractor of the model. Hence one has obtained a nonsingular cosmological model where a single scalar…
Anatomy of localisation protected quantum order on Hilbert space
本文用本征态振幅在Hilbert空间图上的非局域及高点关联刻画局域化保护量子序与纠缠结构，并为分析多体局域化相到遍历相的转变提供新标度途径。
We investigate the continuous quantum measurement of a superconducting qubit undergoing fluorescence. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the fluorescence quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we derive most likely paths between boundary conditions on the state, and compute approximate time correlation functions between all stochastic variables via diagrammatic perturbation theory. We focus on paths that increase in energy during the conti…
Quantum phase transitions reflect singular changes taking place in a many-body ground state, however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. New physical insights into the sub-Ohmic spin-boson model are provided by the coherent state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking, while experiencing strong fluctuations of the order par…
Following our previous paper, Bergeron et al, Smooth quantum dynamics of the mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer framework, we present a further analysis of the dynamical properties of the model. Consistently with the deep quantum regime, we implement the harmonic approximation of the anisotropy potential. We thus obtain manageable dynamical equations. We study the quantum anisotropic oscillations during the bouncing phase of the universe. Neglecting the backreaction from transitions be…
Entanglement production through a cosmological bounce
研究量子宇宙学反弹中高斯初始态的物质—引力纠缠熵演化，发现其先快速上升、下降并趋于稳态，表明纠缠是宏观宇宙特征且不存在纠缠熵第二定律。
Anatomy of Dynamical Quantum Phase Transitions
本文利用量子多体疤痕模型研究动力学量子相变，证明周期性DQPT通常源于简并初态流形中主导贡献的变化，其本质超越两能级系统的拉比振荡图像。
Distinguishing bounce and inflation via quantum signatures from cosmic microwave background
本文提出一种基于CMBR的量子度量（动力学保真度敏感性）来区分暴胀与反弹宇宙学，通过两个相同功率谱模型展示其区分能力，并探讨未来空间任务中的应用。
The Continuous Spontaneous Localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schrödinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the par…
Krylov-space anatomy and spread complexity of a disordered quantum spin chain
通过Krylov基分析无序相互作用自旋链在遍历和MBL相中的量子态扩散复杂度，发现长时间复杂度在遍历相随Fock空间维度线性增长，在MBL相呈次线性增长且态分布呈拉伸指数衰减。
We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entro…
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