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This grant supported work in high energy theoretical physics on quantum field theory by the Principal Investigator Clay Córdova.
Presentation for a seminar at Keio University on aspects of large- N f quantum field theories.
FORTRAN 4 subroutines for coupling coefficients and matrix elements in quantum mechanical theory of angular momentum
A previous paper [Z. Bern et al., Binary dynamics through the fifth power of spin at 𝑂(𝐺 2 ), Phys. Rev. Lett. 130, 201402 (2023)] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through 𝒪(𝛼 2 ) and 𝒪(𝑆 2 ), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity.
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.
We develop an effective theory which describes black holes with quantum mechanical horizons that is valid at scales long compared to the Schwarzschild radius but short compared to the lifetime of the black hole. Our formalism allows one to calculate the quantum mechanical effects in scattering processes involving black hole asymptotic states. We point out that the EFT Wightman functions which describe Hawking radiation in the Unruh vacuum are not Planck suppressed and are actually enhanced relative to those in the Boulware vacuum, for which such radiation is absent. We elaborate on this point showing how the non-Planck suppressed effects of Hawking radiation cancel in classical observables.
Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.
Abstract We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions, ϕ 4 quantum field theories, and Fermi–Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed-matter theory and quantum thermodynamics. However, despite their widespread use, fundamental properties of such circuits are not well understood. Recently, it was found that generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry. This observation raises important open questions: What unitary transformations can be realized with k -local gates that respect a global symmetry? In other words, in the presence of a global symmetry, how does the locality of interactions constrain the possible time evolution of a composite system? In this work, we address these questions for the case of Abelian (commutative) symmetries and develop constructive methods for synthesizing circuits with such symmetries. Remarkably, as a corollary, we find that, while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions observed in the case of non-Abelian symmetries do not apply to circuits with Abelian symmetries. For instance, in circuits with a general non-Abelian symmetry such as SU ( d ) , the unitary realized in a subspace with one irreducible representation (charge) of the symmetry dictates the realized unitaries in multiple other sectors with inequivalent representations of the symmetry. Furthermore, in certain sectors, rather than all unitaries respecting the symmetry, the realizable unitaries are the symplectic or orthogonal subgroups of this group. We prove that none of these restrictions appears in the case of Abelian symmetries. This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries. Published by the American Physical Society 2024
We provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated electromagnetic fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-Λ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. We find that a complex-valued nonlinear coupling coefficient can lead to noises even without linear gain or loss. Lastly, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.
The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.
Quantum entangled photons provide a sensitive probe of many-body interactions and offer a unique experimental portal for quantifying many-body correlations in a material system. In this paper, we present a theoretical demonstration of how photon–photon entanglement can be generated via interactions between coupled qubits. Here, we develop a model for the scattering of an entangled pair of photons from a molecular dimer. We develop a diagrammatic theory for the scattering matrix and show that one can correlate the von Neumann entropy of the outgoing bi-photon wave function with exciton exchange and repulsion interactions. Finally, we conclude by discussing possible experimental scenarios for realizing these ideas.
Quantum mechanical invariance principles dictate the most general operator structure that can be present in the nucleon-nucleon (NN) interaction. Five independent operators appear in the on-shell NN amplitude together with five corresponding coefficient functions. The usual choice for these coefficient functions is known as the NN Wolfenstein amplitudes. We analyze the order-by-order convergence of each of the five NN Wolfenstein amplitudes predicted by a semilocal coordinate space potential implementation of chiral effective field theory (𝜒EFT). We do this at laboratory kinetic energies between 25 and 200 MeV for both neutron-proton and proton-proton scattering. Our analysis uses the Gaussian-process methods developed by the BUQEYE Collaboration to describe the contributions of each 𝜒EFT order, and so yields truncation uncertainties for each Wolfenstein amplitude that are correlated across scattering angles. We combine information on the size of different orders in the EFT to infer the 𝜒EFT breakdown scale for each amplitude, finding, on average, Λ 𝑏 between 750 and 800 MeV. Furthermore, with this choice of Λ 𝑏 , the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.
Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs) [1]. In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number N using scalar ϕ 4 theory in d Euclidean dimensions as an example. We find that the renormalized O(1/N ) corrections to two-and four-point correlators yield perturbative series which are sensitive to the UV cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.
Quantum detector with impinging EM field, discussing photoelectron counting distribution and signal with white noise
Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.
Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.