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On the connection between perturbation theory and new semiclassical expansion in quantum mechanics
Here, it is shown that for the one-dimensional anharmonic oscillator with potential V(x) = ax 2 + bgx 3 + ... = $\frac{1}{g^2}$ $\hat{V}$ (gx), as well as for the radial oscillator V(r) = $\frac{1}{g^2}$ $\hat{V}$ (gr) and for the perturbed Coulomb problem V(r) = $\frac{a}{r}$ + βgr + ... = g $\tilde{V}$ (gr), the Perturbation Theory in powers of the coupling constant g (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ 1/2 for the energies coincide. This is related to the fact that the dynamics developed in two spaces: x (r)-space and gx (gr)-space, lead to the same energy spectra. The equations which govern dynamics in these two spaces, the Riccati-Bloch equation and the Generalized Bloch equation, respectively, are presented. It is shown that the perturbation theory for the logarithmic derivative of the wavefunction in - space leads to (true) semiclassical expansion in powers of $\hbar$ 1/2 ; for the one-dimensional case this corresponds to the flucton calculus for the density matrix in the path integral formalism in Euclidean (imaginary) time proposed by one of the authors. Matching the perturbation theory in powers of g and the semiclassical expansion in powers of $\hbar$ 1/2 for the wavefunction leads to a highly accurate local approximation in the entire coordinate space, its expectation value for the Hamiltonian provides a prescription for the summation of the perturbative (trans)-series.
Parameter-free prediction of phase transition in PbTiO 3 through combination of quantum mechanics and statistical mechanics
Thermodynamics of ferroelectric materials and their ferroelectric to paraelectric (FE-PE) transitions is commonly described by the phenomenological Landau theory and more recently by effective Hamiltonian and various potentials, all with model parameters fitted to experimental or theoretical data. Here, in this work, we show that the zentropy theory, which considers the total entropy of a system as a weighted sum of entropies of configurations that the system may experience and the statistical entropy among the configurations, can predict the FE-PE transition without fitting parameters. For PbTiO 3 , the configurations are identified as the FE configurations with 90- or 180° domain walls in addition to the ground state FE configuration without domain wall. With the domain wall energies predicted from first-principles based on density functional theory in the literature as the only inputs, the FE-PE transition for PbTiO 3 is predicted showing remarkable agreement with experiments, unveiling the microscopic fundamentals of the transition.
A Quantum Mechanical Study of Quartz (101) Interfacial Boundaries
Density functional theory (DFT) calculations were performed on periodic and molecular models to explore the energetics of bonding modes at quartz–quartz interfaces, common grain contacts in sandstones. Four interface types were modeled: H 2 O-mediated, silanol H-bond mediated, O–O peroxide bonds, and siloxane bonds. Each type of interface may exist in the subsurface of the Earth, depending upon water activity, temperature, and pressure, as interfacial structures are stable within DFT molecular dynamics simulations up to 473 K. The results predict interfacial energies SiOSi > SiOOSi > SiOH-6H 2 O > 2SiOH, as expected based on similar bond strengths in other systems. The proposed SiOOSi interface is not generally accounted for in chemomechanical models but could be important in sandstones at depth in the Earth. The implications for intergrain fracturing and H2 generation are discussed.
Quantum Mechanical Methods Predict Accurate Thermodynamics of Biochemical Reactions
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CO 2 Reduction to Methane and Ethylene on a Single-Atom Catalyst: A Grand Canonical Quantum Mechanics Study
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Backaction-evading impulse measurement with mechanical quantum sensors
The quantum measurement of any observable naturally leads to noise added by the act of measurement. Approaches to evade or reduce this noise can lead to substantial improvements in a wide variety of sensors, from laser interferometers to precision magnetometers and more. In this paper, we develop a measurement protocol based upon pioneering work by the gravitational wave community which allows for reduction of added noise from measurement by coupling an optical field to the momentum of a small mirror. As a specific implementation, we present a continuous measurement protocol using a double-ring optomechanical cavity. We demonstrate that, with experimentally relevant parameters, this protocol can lead to significant backaction noise evasion, yielding measurement noise below the standard quantum limit over many decades of frequency.
Hagedorn temperature in large N Majorana quantum mechanics
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Hamiltonian deformations in quantum mechanics, T T ¯ , and the SYK model
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Interference and oscillation in Nambu quantum mechanics
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