More Like this

1. Representation and conservation of angular momentum in the Born–Oppenheimer theory of polyatomic molecules

   https://doi.org/10.1063/5.0143809  

   Littlejohn, Robert ; Rawlinson, Jonathan ; Subotnik, Joseph ( March 2023 , The Journal of Chemical Physics)

   This paper concerns the representation of angular momentum operators in the Born–Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born–Oppenheimer parameter κ = ( m/ M) 1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally,more »it is suggested that the usual Born–Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born–Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.« less
2. Nonadiabatic transition probabilities for quantum systems in electromagnetic fields: Dephasing and population relaxation due to contact with a bath

   https://doi.org/10.1063/5.0138817  

   Jovanovski, Sara D. ; Mandal, Anirban ; Hunt, Katharine L. ( April 2023 , The Journal of Chemical Physics)

   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. Landau and Lifshitz separated Dirac’s excited-state coefficients into a term that follows the adiabatic theorem of Born and Fock and a nonadiabatic term that represents excitation across an energy gap. If the system remains coherent, the two approaches are equivalent. However, differences between the two approaches arise when coupling to a bath causes dephasing, a situation that was not treated by Dirac. For two-level model systems in static electric fields, we add relaxation terms to the Liouville equation for the time derivative of the density matrix. We contrast the results obtained from the two theories. In the analysis based on Dirac’s transition probabilities, the steady state of the system is not an equilibrium state; also, the steady-state population ρkk,s increases with increasing strength of the perturbation and its value depends on the dephasing timemore »T2. In the nonadiabatic theory, the system evolves to the thermal equilibrium with the bath. The difference is not simply due to the choice of basis because the difference remains when the results are transformed to a common basis.« less
3. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers

   https://doi.org/10.1039/d0cp05444e  

   Wang, David Z. ; Gauthier, Aidan Q. ; Siegmund, Ashley E. ; Hunt, Katharine L. ( March 2021 , Physical Chemistry Chemical Physics)

   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. We present results for the spin projections of two entangled qubits, along three axes A , B , and C , with a fixed angle θ between A and B and a range of angles θ ′ between B and C . For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser–Horne–Shimony–Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems.more »We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M . We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M , whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ ′.« less
4. The Weak Gravity Conjecture and axion strings

   https://doi.org/10.1007/JHEP11(2021)004  

   Heidenreich, Ben ; Reece, Matthew ; Rudelius, Tom ( November 2021 , Journal of High Energy Physics)

   A bstract Strong (sublattice or tower) formulations of the Weak Gravity Conjecture (WGC) imply that, if a weakly coupled gauge theory exists, a tower of charged particles drives the theory to strong coupling at an ultraviolet scale well below the Planck scale. This tower can consist of low-spin states, as in Kaluza-Klein theory, or high-spin states, as with weakly-coupled strings. We provide a suggestive bottom-up argument based on the mild p -form WGC that, for any gauge theory coupled to a fundamental axion through a θF ∧ F term, the tower is a stringy one. The charge-carrying string states at or below the WGC scale gM Pl are simply axion strings for θ , with charged modes arising from anomaly inflow. Kaluza-Klein theories evade this conclusion and postpone the appearance of high-spin states to higher energies because they lack a θF ∧ F term. For abelian Kaluza-Klein theories, modified arguments based on additional abelian groups that interact with the Kaluza-Klein gauge group sometimes pinpoint a mass scale for charged strings. These arguments reinforce the Emergent String and Distant Axionic String Conjectures. We emphasize the unproven assumptions and weak points of the arguments, which provide interesting targets for further work. Inmore »particular, a sharp characterization of when gauge fields admit θF ∧ F couplings and when they do not would be immensely useful for particle phenomenology and for clarifying the implications of the Weak Gravity Conjecture.« less
5. $$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization

   https://doi.org/10.1007/JHEP12(2019)119  

   Binder, Damon J. ; Chester, Shai M. ; Pufu, Silviu S. ; Wang, Yifan ( December 2019 , Journal of High Energy Physics)

   A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »limit where N is taken to be large while g YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S 4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.« less