Quantum Physics Commons^™

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The “Quantal Newtonian” Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a “probability amplitude.” A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or “Quantal Newtonian” Laws obeyed by each electron. These Laws, derived from …

The 'Quantal Newtonian' First Law: A Complementary Perspective To The Stationary-State Quantum Theory Of Electrons, Viraht Sahni

Publications and Research

A complementary perspective to the Göttingen-Copenhagen interpretation of stationary-state quantum theory of electrons in an electromagnetic field is described. The perspective, derived from Schrödinger-Pauli theory, is that of the individual electron via its equation of motion or ‘Quantal Newtonian’ First Law. The Law is in terms of ‘classical’ fields experienced by each electron: the sum of the external and internal fields vanishes. The external field is a sum of the electrostatic and Lorentz fields. The internal field is a sum of fields’ representative of Pauli and Coulomb correlations; kinetic effects; electron density; and internal magnetic component. The energy is obtained …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The 'Quantal Newtonian' Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a ‘probability amplitude’. A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper we present a new perspective on such determinism. The ideas are based on the equations of motion or ‘Quantal Newtonian’ Laws obeyed by each electron. These Laws, derived from the …

Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat

Publications and Research

We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.

Wave Function Identity: A New Symmetry For 2-Electron Systems In An Electromagnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

Stationary-state Schrödinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schrödinger-Pauli theory Hamiltonian with a symmetrical binding potential, we report a new symmetry operation of the electronic coordinates. The symmetry operation is such that it leads to the equality of the transformed wave function to the wave function. This equality is referred to as the Wave Function Identity. The symmetry operation is a two-step process: an interchange of the spatial coordinates of the electrons whilst keeping their spin moments unchanged, followed by an inversion. The Identity …

Experimental Observation Of Topological Z2 Excitonpolaritons In Transition Metal Dichalcogenide Monolayers, Mengyao Li, Ivan Sinev, Fedor Benimetskiy, Tatyana Ivanova, Ekaterina Khestanova, Svetlana Kiriushechkina, Anton Vakulenko, Sriram Guddala, Maurice Skolnick, Vinod M. Menon, Dmitry Krizhanovskii, Andrea Alù, Anton Samusev, Alexander B. Khanikaev

Publications and Research

The rise of quantum science and technologies motivates photonics research to seek new platforms with strong light-matter interactions to facilitate quantum behaviors at moderate light intensities. Topological polaritons (TPs) offer an ideal platform in this context, with unique properties stemming from resilient topological states of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) as a promising platform for topological polaritonics. We show that the strong coupling between topological photonic modes of the metasurface and excitons in TMDs yields a topological polaritonic Z₂ phase. We experimentally confirm the emergence of one-way …

Enhanced Nonlinear Interaction Of Polaritons Via Excitonic Rydberg States In Monolayer Wse2, Jie Gu, Valentin Walther, Lutz Waldecker, Daniel Rhodes, Archana Raja, James C. Hone, Tony F. Heinz, Stéphane Kéna-Cohen, Thomas Pohl, Vinod M. Menon

Publications and Research

Strong optical nonlinearities play a central role in realizing quantum photonic technologies. Exciton-polaritons, which result from the hybridization of material excitations and cavity photons, are an attractive candidate to realize such nonlinearities. While the interaction between ground state excitons generates a notable optical nonlinearity, the strength of such interactions is generally not sufficient to reach the regime of quantum nonlinear optics. Excited states, however, feature enhanced interactions and therefore hold promise for accessing the quantum domain of single-photon nonlinearities. Here we demonstrate the formation of exciton-polaritons using excited excitonic states in monolayer tungsten diselenide (WSe₂) embedded in a …

Triplet 23S State Of A Quantum Dot In A Magnetic Field: A 'Quantal Newtonian' First Law Study, Marlina Slamet, Viraht Sahni

Publications and Research

The triplet 2³S state of a 2-electron 2-dimensional quantum dot in a magnetic field is studied via a complementary perspective of Schrödinger-Pauli theory. The perspective is that of the individual electron via its equation of motion or ‘Quantal Newtonian’ first law. According to the law, each electron experiences an external and internal field, the sum of which vanishes. The external field is the sum of the binding and Lorentz fields. The internal field is a sum of the electron-interaction, kinetic, differential density, and internal magnetic fields. The energy is expressed in integral virial form in terms of these …

Exclusion Statistics For Particles With A Discrete Spectrum, Stéphane Ouvry, Alexios P. Polychronakos

Publications and Research

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a …

Schrödinger-Pauli Theory Of Electrons: New Perspectives, Viraht Sahni

Publications and Research

The Schrödinger-Pauli (SP) theory of electrons in an electromagnetic field explicitly accounts for the electron spin moment. The many-electron theory is complemented via a new descriptive perspective viz. that of the individual electron via its equation of motion or ‘Quantal Newtonian’ first law. The law is in terms of ‘classical’ fields whose sources are quantum mechanical expectation values of Hermitian operators taken with respect to the system wave function. The law states that each electron experiences an external and an internal field, the sum of which vanish. The external field is the sum of the binding electrostatic and a Lorentz …

Double Inclusive Small-X Gluon Production And Their Azimuthal Correlations In A Biased Ensemble, Gary Kapilevich

Publications and Research

We consider double gg → g production in the presence of a bias on the unintegrated gluon distribution of the colliding hadrons or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal correlations, for a few simple examples of biases.

Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan

Publications and Research

The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …

Master Integrals For The Two-Loop, Non-Planar Qcd Corrections To Top-Quark Pair Production In The Quark-Annihilation Channel, Matteo Becchetti, Roberto Bonciani, Valerio Casconi, Andrea Ferroglia, Simone Lavacca, Andreas Von Manteuffel

Publications and Research

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator ε and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.

Exploring A Practical Development Of Quantum Computing, Juliano A. Everett, Andrea N. Zambrano, Carlos Aguayza

Publications and Research

Tasked with describing a Quantum architecture (Superconducting loops), we additionally explored how the chosen architecture is used, developed, and how one could get started in understanding the way in which some quantum algorithms work with this architecture through Python and IBM's tools (Qiskit and IBM Q Experience).

Optical Detection And Storage Of Entanglement In Plasmonically Coupled Quantum-Dot Qubits, M. Otten, S.K. Gray, German Kolmakov V

Publications and Research

Recent proposals and advances in quantum simulations, quantum cryptography, and quantum communications substantially rely on quantum entanglement formation. Contrary to the conventional wisdom that dissipation destroys quantum coherence, coupling with a dissipative environment can also generate entanglement. We consider a system composed of two quantum-dot qubits coupled with a common, damped surface plasmon mode; each quantum dot is also coupled to a separate photonic cavity mode. Cavity quantum electrodynamics calculations show that upon optical excitation by a femtosecond laser pulse, entanglement of the quantum-dot excitons occurs, and the time evolution of the g(2) pair correlation function of the cavity photons …

Peculiar Optical Properties Of Bilayer Silicene Under The Influence Of External Electric And Magnetic Fields, Thi-Nga Do, Godfrey Gumbs, Po-Hsin Shih, Danhong Huang, Chih-Wei Chiu, Chia-Yun Chen, Ming-Fa Lin

Publications and Research

We conduct a comprehensive investigation of the effect of an applied electric field on the optical and magneto-optical absorption spectra for AB-bt (bottom-top) bilayer silicene. The generalized tightbinding model in conjunction with the Kubo formula is efficiently employed in the numerical calculations. The electronic and optical properties are greatly diversified by the buckled lattice structure, stacking configuration, intralayer and interlayer hopping interactions, spin-orbital couplings, as well as the electric and magnetic fields (Ez ˆz & Bz ˆz ). An electric field induces spin-split electronic states, a semiconductor-metal phase transitions and the Dirac cone formations in different valleys, leading to the …

New Perspectives On The Schrödinger-Pauli Theory Of Electrons: Part Ii: Application To The Triplet State Of A Quantum Dot In A Magnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

The Schrödinger-Pauli (SP) theory of electrons in the presence of a static electromagnetic field can be described from the perspective of the individual electron via its equation of motion or 'Quantal Newtonian' first law. The law is in terms of 'classical' fields whose sources are quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. The law states that the sum of the external and internal fields experienced by each electron vanishes. The external field is the sum of the binding electrostatic and Lorentz fields. The internal field is the sum of fields representative of properties of …

New Perspectives On The Schrödinger-Pauli Theory Of Electrons: Part I, Viraht Sahni

Publications and Research

Schrödinger-Pauli (SP) theory is a description of electrons in the presence of a static electromagnetic field in which the interaction of the magnetic field with both the orbital and spin moments is explicitly considered. The theory is described from the new perspective of the individual electron via its equation of motion or ‘Quantal Newtonian’ first law. The law is in terms of ‘classical’ fields whose sources are quantum mechanical expectation values of Hermitian operators taken with respect to the system wave function. The law states that each electron experiences an external and an internal field, the sum of which vanish. …

Computational Techniques For Scattering Amplitudes, Juliano A. Everett

Publications and Research

Scattering amplitudes in quantum field theory can be described as the probability of a scattering process to happen within a high energy particle interaction, as well as a bridge between experimental measurements and the prediction of the theory.

In this research project, we explore the Standard Model of Particle Theory, it’s representation in terms of Feynman diagrams and the algebraic formulas associated with each combination.

Using the FeynArts program as a tool for generating Feynman diagrams, we evaluate the expressions of a set of physical processes, and explain why these techniques become necessary to achieve this goal.

Study Of The Kinetic Energy Densities Of Electrons As Applied To Quantum Dots In A Magnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

There are three expressions for the kinetic energy density t(r) expressed in terms of its quantal source, the single‐particle density matrix: t_A(r), the integrand of the kinetic energy expectation value; t_B(r), the trace of the kinetic energy tensor; t_C(r), a virial form in terms of the 'classical' kinetic field. These kinetic energy densities are studied by application to 'artificial atoms' or quantum dots in a magnetic field in a ground and excited singlet state. A comparison with the densities for natural atoms and molecules in their ground state is made. The near nucleus …

The Diverse Magneto-Optical Selection Rules In Bilayer Black Phosphorus, Jhao-Ying Wu, Szu-Chao Chen, Thi-Nga Do, Wu-Pei Su, Godfrey Gumbs, Ming-Fa Lin

Publications and Research

The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A uniform perpendicular electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and …

Kinetic Effects In 2d And 3d Quantum Dots: Comparison Between High And Low Electron Correlation Regimes, Marlina Slamet, Viraht Sahni

Publications and Research

Kinetic related ground state properties of a two-electron 2D quantum dot in a magnetic field and a 3D quantum dot (Hooke's atom) are compared in the Wigner high (HEC) and low (LEC) electron correlation regimes. The HEC regime corresponds to low densities sufficient for the creation of a Wigner molecule. The LEC regime densities are similar to those of natural atoms and molecules. The results are determined employing exact closed-form analytical solutions of the Schrödinger-Pauli and Schrödinger equations, respectively. The properties studied are the local and nonlocal quantal sources of the density and the single particle density matrix; the kinetic …

Resummation For (Boosted) Top-Quark Pair Production At Nnlo+Nnll' In Qcd, Michał Czakon, Andrea Ferroglia, David Heymes, Alexander Mitov, Ben D. Pecjak, Darren J. Scott, Xing Wang, Li Lin Yang

Publications and Research

We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL′ accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL′ accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the $M_{t\bar{t}}$ and top-quark $p_T$ distributions in the boosted regime where fixed order calculations may become strongly dependent on the choice of dynamic scales. With the …

Comparative Study Of Qubits, Juliano A. Everett, Mubinjon Satymov, Zechariah Ilmot

Publications and Research

In quantum computing, a quantum bit ("qubit") is a unit of quantum information. A qubit is a two-level quantum system. The developing of qubits with optimal properties, related to quantum entanglement and possibilities of control the states of qubits, is very important for quantum computing applications. We analyzed various types of qubits. There are at least five major quantum computing approaches being explored worldwide: silicon spin qubits, ion traps, superconducting loops, diamond vacancies and topological qubits. We compared the advantages and disadvantages in the properties of all these qubits for applications for quantum computing. We analyzed possible strategies to improve …

Dissipation Effects In Schrödinger And Quantal Density Functional Theories Of Electrons In An Electromagnetic Field, Xiao-Yin Pan, Viraht Sahni

Publications and Research

Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in which the electron mass is time-dependent. The perspective is that of the individual electron: the corresponding equation of motion for the electron or time-dependent differential virial theorem—the ‘Quantal Newtonian’ second law—is derived. According to the law, each electron experiences an external field comprised of a binding electric field, the Lorentz field, and the electromagnetic field. In addition, …

Higher Cluster Categories And Qft Dualities, Sebastián Franco, Gregg Musiker

Publications and Research

We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m + 1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.

Octet Baryons In Large Magnetic Fields, Amol Deshmukh, Brian C. Tiburzi

Publications and Research

Magnetic properties of octet baryons are investigated within the framework of chiral perturbation theory. Utilizing a power counting for large magnetic fields, the Landau levels of charged mesons are treated exactly giving rise to baryon energies that depend nonanalytically on the strength of the magnetic field. In the small-field limit, baryon magnetic moments and polarizabilities emerge from the calculated energies. We argue that the magnetic polarizabilities of hyperons provide a testing ground for potentially large contributions from decuplet pole diagrams. In external magnetic fields, such contributions manifest themselves through decuplet-octet mixing, for which possible results are compared in a few …

Prompt Photon-Jet Angular Correlations At Central Rapidities In P + A Collisions, Sanjin Benić, Adrian Dumitru

Publications and Research

Photon-jet azimuthal correlations in proton-nucleus collisions are a promising tool for gaining information on the gluon distribution of the nucleus in the regime of nonlinear color fields. We compute such correlations from the process $g → q\bar{q}γ$ in the rapidity regime where both the projectile and target light-cone momentum fractions are small. By integrating over the phase space of the quark which emits the photon, subject to the restriction that the photon picks up most of the transverse momentum (to pass an isolation cut), we effectively obtain a g + A → qγ process. For nearly back-to-back photon-jet configurations we …

Elliptic Genera Of 2d (0,2) Gauge Theories From Brane Brick Models, Sebastian Franco, Dongwook Ghim, Sangmin Lee, Rak-Kyeong Seong

Publications and Research

We compute the elliptic genus of abelian 2d (0, 2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a match with the elliptic genus of the non-linear sigma model on the same Calabi-Yau background, which is computed using a new localization formula. The matching implies that the quantum effects do not drastically alter the correspondence between the geometry and the 2d (0, 2) gauge theory. In theories whose matter sector suffers from abelian gauge anomaly, we propose an ansatz for an anomaly …

Schrödinger Theory Of Electrons In Electromagnetic Fields: New Perspectives, Viraht Sahni, Xiao-Yin Pan

Publications and Research

The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent "Quantal Newtonian" law (or differential virial theorem). (The time-independent law, a special case, provides a similar description of stationary-state theory). These laws are in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the …