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Constrained variation method in molecular quantum mechanics, presenting wave function, degree of constraint and energy loss values for lithium hydride molecule
Quantum mechanical relation for magnetized electron gas in constant magnetic field and thermal equilibrium
In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.
Experiments have shown that graphene-supported Ni-single atom catalysts (Ni-SACs) provide a promising strategy for the electrochemical reduction of CO 2 to CO, but the nature of the Ni sites (Ni-N 2 C 2 , Ni-N 3 C 1 , Ni-N 4 ) in Ni-SACs has not been determined experimentally. Here, we apply the recently developed grand canonical potential kinetics (GCP-K) formulation of quantum mechanics to predict the kinetics as a function of applied potential (U) to determine faradic efficiency, turn over frequency, and Tafel slope for CO and H 2 production for all three sites. We predict an onset potential (at 10 mA cm –2 ) U onset = –0.84 V (vs. RHE) for Ni-N 2 C 2 site and U onset = –0.92 V for Ni-N 3 C 1 site in agreement with experiments, and U onset = –1.03 V for Ni-N 4 . We predict that the highest current is for Ni-N 4 , leading to 700 mA cm –2 at U = –1.12 V. To help determine the actual sites in the experiments, we predict the XPS binding energy shift and CO vibrational frequency for each site.
Quantum mechanical calculations for gas phase bimolecular exchange reactions between hydrogen and bromine
Phase shift method using integration of quantum- mechanical Hamilton-Jacobi equation applied to particles interacting through Lennard-Jones potential
Many fundamental questions at the interface of quantum mechanics, gravity, and measurement remain relatively unexplored in the laboratory. These include whether spatial superpositions experience gravitational redshift, how the quantum Zeno effect propagates through entangled systems, and whether quantum information is globally conserved or fundamentally lost during measurement-induced wavefunction collapse. In this colloquium, I will discuss how superconducting qubits—developed primarily for quantum computing—can be repurposed as ultra sensitive detectors to probe these questions and to search for low-energy particle interactions. I will describe my work at Fermilab on stabilizing these devices to the level required for next-generation qubit-based sensors. This includes mitigating decoherence from infrared radiation and cosmic rays, using machine-learning techniques to accelerate superconducting qubit design, and leveraging the quantum Zeno effect to improve coherence times and suppress qubit frequency fluctuations. Together, these advances point toward a new class of quantum sensors capable of testing fundamental physics.
We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection coefficient for various potentials and compare to physical expectations. This includes an application of semidefinite programming to solving a half line Schrodinger problem with arbitrary Robin boundary conditions. Finally, the WKB approximation is used to numerically determine the scattering behavior of the exponential potential of Liouville theory. Published by the American Physical Society 2024
Optimum signal reception using quantum-mechanical communication theory
A detailed study of the influence of quantum effects in the inversion layer on the random dopant induced threshold voltage fluctuations and lowering in sub 0.1 micron MOSFETs has been performed. This has been achieved using a full 3D implementation of the density gradient (DG) formalism incorporated in our previously published 3D 'atomistic' simulation approach. This results in a consistent, fully 3D, quantum mechanical picture which implies not only the vertical inversion layer quantisation but also the lateral confinement effects manifested by current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical fluctuations, is an increase in both threshold voltage fluctuations and lowering.
We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S 1 . We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even N and global inconsistency for odd N. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.
The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantum mechanics. A numerical solution to the related rate equations describing the probabilities of occupation of the electron's energy states is put forth along with the expected errors involved. The quantum-mechanical approach is found to predict a significant amount of energy broadening with time for an initially monoenergetic electron beam entering a region of an intense magnetic field as long as the product of initial energy and magnetic field is of order 50 MG BeV or larger.
In this note, I review a recent approach to quantum gravity that “gravitizes” quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also have promise in emerging gravity in near-flat geometries.
We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, and determine finite temperature observables that interpolate between available analytic results in the low and high temperature limits respectively. We also obtain bootstrap bounds on thermal phase transition as well as preliminary results in the ungauged two-matrix quantum mechanics.
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic structure, thereby unifying the axioms that traditionally distinguish the treatment of spacelike and timelike separations. Standard quantum evolution can be recovered from timelike correlators, defined by means of a quantum action operator, a quantum version of the action of classical mechanics. The corresponding map also provides an alternative perspective on the path integral formulation that, in the case of fermions, does not require the use of Grassmann variables. In addition, the formalism can be interpreted in terms of generalized quantum states, codifying both the conventional information of a quantum system at a given time and its evolution. We show that these states are solutions to a quantum principle of stationary action grounded in timelike correlations and pseudo-entropies.
Accurate values of phase shifts calculated by integration of quantum mechanical Hamilton- Jacobi equation
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Accurate understanding of Ultraviolet–visible (UV–Vis) spectra is critical for highthroughput design of compounds for drug discovery. Experimentally determining UV–Vis spectra can become expensive when dealing with a large quantity of novel molecules. This provides us an opportunity to drive computational advances in molecular property predictions using quantum mechanics and machine learning. In this work, we use both Quantum Mechanically (QM) predicted and measured UV–Vis spectra as input to modify four different machine learning architectures: UVvis-SchNet, UVvis- DTNN, UVvis-Transformer, and UVvis-MPNN. Here we find that the UVvis-MPNN model outperforms the other models when using optimized 3D coordinates and QM predicted spectra as input features. This model has the highest performance for predicting UVVisible spectra with a training RMSE of 0.06 and validation RMSE of 0.08.