Nonadiabatic transition probabilities for quantum systems in electromagnetic fields: Dephasing and population relaxation due to contact with a bath.

We contrast Dirac's theory of transition probabilities and the theory of nonadiabatic transition probabilities, applied to a perturbed system that is coupled to a bath. In Dirac's analysis, the presence of an excited state |k0⟩ in the time-dependent wave function constitutes a transition. In the nonadiabatic theory, a transition occurs when the wave function develops a term that is not adiabatically connected to the initial state.

Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states.

Using IBM's publicly accessible quantum computers, we have analyzed the entropies of Schrödinger's cat states, which have the form = (1/2) [|0 0 0⋯0〉 + |1 1 1⋯1〉]. We have obtained the average Shannon entropy of the distribution over measurement outcomes from 75 runs of 8192 shots, for each of the numbers of entangled qubits, on each of the quantum computers tested. For the distribution over N fault-free measurements on pure cat states, would approach one as N → ∞, independent of the number of qubits; but we have found that varies nearly linearly with the number of qubits .

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response.

Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities.

For a quantum system in a time-dependent perturbation, we prove that the variance in the energy depends entirely on the nonadiabatic transition probability amplitudes b(t). Landau and Lifshitz introduced the nonadiabatic coefficients for the excited states of a perturbed quantum system by integrating by parts in Dirac's expressions for the coefficients c (t) of the excited states to first order in the perturbation. This separates c (t) for each state into an adiabatic term a (t) and a nonadiabatic term b (t).

The interaction-induced dipole of H-H: New ab initio results and spherical tensor analysis.

We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the exponential operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state.

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u.

Nonadiabatic transition probabilities in a time-dependent Gaussian pulse or plateau pulse: Toward experimental tests of the differences from Dirac's transition probabilities.

For a quantum system subject to a time-dependent perturbing field, Dirac's analysis gives the probability of transition to an excited state |k⟩ in terms of the norm square of the entire excited-state coefficient c(t) in the wave function. By integrating by parts in Dirac's equation for c(t) at first order, Landau and Lifshitz separated c (t) into an adiabatic term a (t) that characterizes the gradual adjustment of the ground state to the perturbation and a nonadiabatic term b (t) that depends explicitly on the time derivative of the perturbation at times t' ≤ t. Landau and Lifshitz stated that the probability of transition in a pulsed perturbation is given by |b(t)|, rather than by |c(t)|.

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms.

For a perturbed quantum system initially in the ground state, the coefficient c(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term a(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H without transitions; a(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term b(t) describes excitation into another quantum state k; b(t) is obtained as an integral containing the time derivative of the perturbation.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field.

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field.

Non-adiabatic current densities, transitions, and power absorbed by a molecule in a time-dependent electromagnetic field.

The energy of a molecule subject to a time-dependent perturbation separates completely into adiabatic and non-adiabatic terms, where the adiabatic term reflects the adjustment of the ground state to the perturbation, while the non-adiabatic term accounts for the transition energy [A. Mandal and K. L.

Quantum mechanical calculation of the collision-induced absorption spectra of N2-N2 with anisotropic interactions.

We present quantum mechanical calculations of the collision-induced absorption spectra of nitrogen molecules, using ab initio dipole moment and potential energy surfaces. Collision-induced spectra are first calculated using the isotropic interaction approximation. Then, we improve upon these results by considering the full anisotropic interaction potential.

Ground and excited states of vanadium hydroxide isomers and their cations, VOH(0,+) and HVO(0,+).

Employing correlation consistent basis sets of quadruple-zeta quality and applying both multireference configuration interaction and single-reference coupled cluster methodologies, we studied the electronic and geometrical structure of the [V,O,H](0,+) species. The electronic structure of HVO(0,+) is explained by considering a hydrogen atom approaching VO(0,+), while VOH(0,+) molecules are viewed in terms of the interaction of V(+,2+) with OH(-). The potential energy curves for H-VO(0,+) and V(0,+)-OH have been constructed as functions of the distance between the interacting subunits, and the potential energy curves have also been determined as functions of the H-V-O angle.

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: complete separation and physical interpretation.

When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state ∣0> of an unperturbed Hamiltonian H(0), the wave function acquires excited-state components ∣k> with coefficients c(k)(t) exp(-iE(k)t/ℏ), where E(k) denotes the energy of the unperturbed state ∣k>. It is well known that each coefficient c(k)(t) separates into an adiabatic term a(k)(t) that reflects the adjustment of the ground state to the perturbation--without actual transitions--and a nonadiabatic term b(k)(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants.

Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: a new ab initio dipole surface for high-temperature applications.

We report new ab initio results for the interaction-induced dipole moments Δμ of hydrogen molecules colliding with helium atoms. These results are needed in order to calculate collision-induced absorption spectra at high temperatures; applications include modeling the radiative profiles of very cool white dwarf stars, with temperatures from 3500 K to 9000 K. We have evaluated the dipoles based on finite-field calculations, with coupled cluster methods in MOLPRO 2006 and aug-cc-pV5Z (spdfg) basis sets for both the H and He centers.

Infrared absorption by collisional H2-He complexes at temperatures up to 9000 K and frequencies from 0 to 20,000 cm(-1).

Quantum chemical methods have been used elsewhere to obtain the potential energy surface (PES) and the induced dipole surface (IDS) of H(2)-He collisional complexes at eight different H-H bond distances, fifteen atom-molecule separations, and 19 angular orientations each [X. Li, A. Mandal, E.

Ab initio investigation of titanium hydroxide isomers and their cations, TiOH(0,+) and HTiO(0,+).

We studied the electronic and geometrical structure of the [Ti, O, H](0,+) species, using large basis sets and both single-reference coupled cluster and multireference configuration interaction methodologies. The electronic structure of HTiO(0,+) is interpreted qualitatively in terms of a hydrogen atom bonding to TiO(0,+), while the structure of TiOH(0,+) is interpreted in terms of Ti(+,2+) bonding to OH(-). Potential energy profiles are reported as functions of the Ti-OH and H-TiO bond lengths, and of the H-Ti-O angle.

First-principles calculations of the electronic and geometrical structures of neutral [Sc,O,H] molecules and the monocations, ScOH(0,+) and HScO(0,+).

Using multireference configuration interaction and coupled-cluster methodologies, with quadruple-ζ basis sets, we explored the potential energy surfaces of the ground and excited states of the neutral and cationic triatomics [Sc,O,H](0,+). In its ground state, the neutral species is trapped into either a linear ScOH or a bent HScO conformation; these two minima are approximately equal in energy and separated by a barrier of 40 kcal/mol. The linear ScOH structure is preferred by the excited states of the neutral species and by all of the electronic states of the charged molecular systems that we studied in this work.

Collision-induced absorption by H2 pairs: from hundreds to thousands of kelvin.

An interaction-induced dipole surface (IDS) and a potential energy surface (PES) of collisionally interacting molecular hydrogen pairs H(2)-H(2) was recently obtained using quantum chemical methods (Li, X.; et al. Computational Methods in Science and Engineering, ICCMSE.

Derivatives of the polarization propagator including orbital relaxation effects.

In this article, we relate derivatives of the polarization propagator used in many-body theory to the nonlinear (quadratic) polarization propagator, and we relate derivatives of the quadratic polarization propagator to the nonlinear propagator of the next higher order, the cubic polarization propagator. We restrict the analysis to differentiation with respect to parameters eta for which the derivative of the Hamiltonian can be written as a sum of one-electron operators. Geometrical derivatives are obtained by specializing to the parameter eta to the alpha coordinate of nucleus I.