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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Localization of quantum Bernoulli noises

The family (∂{sub k},∂{sub k}{sup *}){sub k≥0} of annihilation and creation operators acting on square integrable functionals of a Bernoulli process Z= (Z{sub k}){sub k⩾0} can be interpreted as quantum Bernoulli noises. In this note we consider the operator family (ℓ{sub k},ℓ{sub k}{sup *}){sub k≥0}, where ℓ{sub k}=∂{sub k}E{sub k} with E{sub k} being the conditional expectation (operator) given σ-field σ(Z{sub j}; 0 ⩽j⩽k). We show that ℓ{sub k} (resp. ℓ{sub k}{sup *}) is essentially a kind of localization of the annihilation operator ∂{sub k} (resp. creation operator ∂{sub k}{sup *}). We examine properties of the family (ℓ{sub k},ℓ{sub k}{sup *}){sub k≥0} and prove, among other things, that ℓ{sub k} and ℓ{sub k}{sup *} satisfy a local canonical anti-communication relation and (ℓ{sub k}{sup *}){sub k≥0} forms a mutually orthogonal operator sequence although each ℓ{sub k} is not a projection operator. We find that the operator series Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}Xℓ{sub k} converges in the strong operator topology for each bounded operator X acting on square integrable functionals of Z. In particular we get an explicit sum of the operator series Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}ℓ{sub k}. A useful norm estimate on Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}Xℓ{sub k} is also obtained. Finally we show applications of our main results to quantum dynamical semigroups and quantum probability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states

We revise the unireps. of U(2, 2) describing conformal particles with continuous mass spectrum from a many-body perspective, which shows massive conformal particles as compounds of two correlated massless particles. The statistics of the compound (boson/fermion) depends on the helicity h of the massless components (integer/half-integer). Coherent states (CS) of particle-hole pairs (“excitons”) are also explicitly constructed as the exponential action of exciton (non-canonical) creation operators on the ground state of unpaired particles. These CS are labeled by points Z (2×2 complex matrices) on the Cartan-Bergman domain D₄=U(2,2)/U(2)², and constitute a generalized (matrix) version of Perelomov U(1, 1) coherent states labeled by points z on the unit disk D₁=U(1,1)/U(1)². First, we follow a geometric approach to the construction of CS, orthonormal basis, U(2, 2) generators and their matrix elements and symbols in the reproducing kernel Hilbert space H{sub λ}(D₄) of analytic square-integrable holomorphic functions on D₄, which carries a unitary irreducible representation of U(2, 2) with index λϵN (the conformal or scale dimension). Then we introduce a many-body representation of the previous construction through an oscillator realization of the U(2, 2) Lie algebra generators in terms of eight boson operators with constraints. This particle picture allows us for a physical interpretation of our abstract mathematical construction in the many-body jargon. In particular, the index λ is related to the number 2(λ – 2) of unpaired quanta and to the helicity h = (λ – 2)/2 of each massless particle forming the massive compound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Grassmann phase space methods for fermions. II. Field theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Grassmann phase space theory and the Jaynes–Cummings model

The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are often developed. However, atomic spin operators satisfy the standard angular momentum commutation rules rather than the commutation rules for bosonic annihilation and creation operators, and are in fact second order combinations of fermionic annihilation and creation operators. Though phase space methods in which the fermionic operators are represented directly by c-number phase space variables have not been successful, the anti-commutation rules for these operators suggest the possibility of using Grassmann variables—which have similar anti-commutation properties. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of phase space methods in quantum optics to treat fermionic systems by representing fermionic annihilation and creation operators directly by Grassmann phase space variables is rather rare. This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the TLA) can be used to treat the Jaynes–Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker–Planck equation involving both left and right Grassmann differentiations can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, in which the correspondence rules for the bosonic operators are non-standard and hence the Fokker–Planck equation is also unusual. Initial conditions, such as those above for initially uncorrelated states, are discussed and used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enable the six coupled equations for the new c-number functions–that are also equivalent to the canonical Grassmann distribution function–to be solved analytically, based on an ansatz from an earlier paper by Stenholm. It is then shown that the distribution function is exactly the same as that determined from the well-known solution based on coupled amplitude equations. In quantum–atom optics theories for many atom bosonic and fermionic systems are needed. With large atom numbers, treatments must often take into account many quantum modes—especially for fermions. Generalisations of phase space distribution functions of phase space variables for a few modes to phase space distribution functionals of field functions (which represent the field operators, c-number fields for bosons, Grassmann fields for fermions) are now being developed for large systems. For the fermionic case, the treatment of the simple two mode problem represented by the Jaynes–Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for fermionic applications in quantum–atom optics. -- Highlights: •Novel phase space theory of the Jaynes–Cummings model using Grassmann variables. •Fokker–Planck equations solved analytically. •Results agree with the standard quantum optics treatment. •Grassmann phase space theory applicable to fermion many-body problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Phase space theory of Bose-Einstein condensates and time-dependent modes

A phase space theory approach for treating dynamical behaviour of Bose-Einstein condensates applicable to situations such as interferometry with BEC in time-dependent double well potentials is presented. Time-dependent mode functions are used, chosen so that one, two, Horizontal-Ellipsis highly occupied modes describe well the physics of interacting condensate bosons in time dependent potentials at well below the transition temperature. Time dependent mode annihilation, creation operators are represented by time dependent phase variables, but time independent total field annihilation, creation operators are represented by time independent field functions. Two situations are treated, one (mode theory) is where specific mode annihilation, creation operators and their related phase variables and distribution functions are dealt with, the other (field theory) is where only field creation, annihilation operators and their related field functions and distribution functionals are involved. The field theory treatment is more suitable when large boson numbers are involved. The paper focuses on the hybrid approach, where the modes are divided up between condensate (highly occupied) modes and non-condensate (sparsely occupied) modes. It is found that there are extra terms in the Ito stochastic equations both for the stochastic phases and stochastic fields, involving coupling coefficients defined via overlap integrals between mode functions and their time derivatives. For the hybrid approach both the Fokker-Planck and functional Fokker-Planck equations differ from those derived via the correspondence rules, the drift vectors are unchanged but the diffusion matrices contain additional terms involving the coupling coefficients. Results are also presented for the combined approach where all the modes are treated as one set. Here both the Fokker-Planck and functional Fokker-Planck equations are exactly the same as those derived via the correspondence rules. However, although the Ito stochastic field equations are also unchanged, the Ito equations for the stochastic phases contain an extra classical term involving the coupling coefficients. - Highlights: Black-Right-Pointing-Pointer Wigner, P+ representations used for condensate and non-condensate bosons, respectively. Black-Right-Pointing-Pointer Time dependence of modes leads to novel Fokker-Planck and Ito equations. Black-Right-Pointing-Pointer Field theory and separate mode treatments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

General displaced SU(1, 1) number states: Revisited

The most general displaced number states, based on the bosonic and an irreducible representation of the Lie algebra symmetry of su(1, 1) and associated with the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well-known Barut-Girardello coherent and number states, respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of these states is included. Significant are their squeezing properties and anti-bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Violation of the area law and long-range correlations in infinite-dimensional-matrix product states

We propose to construct a family of states of one-dimensional spin chains by replacing the finite-dimensional matrices in matrix product states by infinite-dimensional operators constructed from bosonic annihilation and creation operators. The resulting states are demonstrated to violate the area law and to exhibit long-range correlations. In addition, we propose an efficient way to prepare the states experimentally, in which the spins interact sequentially with an ancilla system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Construction of a fermionic vacuum and the fermionic operators of creation and annihilation in the theory of algebraic spinors

In complex modules over real Clifford algebras of even dimension, fermionic variables, which are an analogue of the Witt basis, are introduced. Based on them, primitive idempotents are built which represent the equivalent Clifford vacua. It is shown that modules of algebras are decomposed into a direct sum of minimal left ideals, generated by these idempotents, and that fermionic variables can be considered as more fundamental mathematical objects than spinors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

The coordinate coherent states approach revisited

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies that the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor. - Highlights: Black-Right-Pointing-Pointer Suggest a canonical quantization in the coordinate coherent states approach. Black-Right-Pointing-Pointer Prove the validity of the concept of point particles. Black-Right-Pointing-Pointer Apply the canonical quantization to the Unruh effect and Hawking radiation. Black-Right-Pointing-Pointer Find no deformations in the Unruh temperature and Hawking temperature. Black-Right-Pointing-Pointer Provide the modified spectra of the Unruh effect and Hawking radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement

The universal nilpotent computational rewrite system (UNCRS) is shown to formalize an irreversible process of evolution in conformity with the First, Second and Third Laws of Thermodynamics, in terms of a single algebraic creation operator (ikE+ip+jm) which delivers the whole quantum mechanical language apparatus, where k, i, j are quaternions units and E, p, m are energy, momentum and rest mass. This nilpotent evolution describes 'a dynamic zero totality universe' in terms of its fermion states (each of which, by Pauli exclusion, is unique and nonzero), where, together with their boson interactions, these define physics at the fundamental level. (The UNCRS implies that the inseparability of objects and fields in the quantum universe is based on the fact that the only valid mathematical representations are all automorphisms of the universe itself, and that this is the mathematical meaning of quantum entanglement. It thus appears that the nilpotent fermion states are in fact what is called the splitting field in Quantum Mechanics of the Galois group which leads to the roots of the corresponding algebraic equation, and concerns in this case the alternating group of even permutations which are themselves automorphisms). In the nilpotent evolutionary process: (i) the Quantum Carnot Engine (QCE) extended model of thermodynamic irreversibility, consisting of a single heat bath of an ensemble of Standard Model elementary particles, retains a small amount of quantum coherence / entanglement, so as to constitute new emergent fermion states of matter, and (ii) the metric (E{sup 2}-p{sup 2}m{sup 2}) = 0 ensures the First Law of the conservation of energy operates at each nilpotent stage, so that (iii) prior to each creation (and implied corresponding annihilation / conserve operation), E and m can be postulated to constitute dark energy and matter respectively. It says that the natural language form of the rewrite grammar of the evolution consists of the well known precepts of the Laws of Thermodynamics, formalized by the UNCRS regress, so as to become (as UNCRS rewrites already published at CASYS), firstly the Quantum Laws of Physics in the form of the generalized Dirac equation and later at higher stages of QCE ensemble complexity, the Laws of Life in the form of Nature's (DNA / RNA genetic) Code and then subsequently those of Intelligence and Consciousness (Nature's Rules).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Noncommutative Pfaffians and classification of states of five-dimensional quasi-spin

Noncommutative Pfaffians associated with an orthogonal algebra o{sub N} are some special elements of the universal enveloping algebra U(o{sub N}). Using Pfaffians we construct the fourth quantum number which together with the naturally defined three quantum numbers allows to classify the states of a five-dimensional quasi-spin. The Pfaffians are treated as creation operators for the new quantum number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Quantum state engineering by a coherent superposition of photon subtraction and addition

We study a coherent superposition ta+ra{sup {dagger} }of field annihilation and creation operators acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Dual origin of pairing in nuclei

The pairing correlations of the nucleus {sup 120}Sn are calculated by solving the Nambu–Gor’kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong {sup 1}S{sub 0} short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v{sub p}{sup bare}) and long-range (v{sub p}{sup ind}) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Quantum Markov semigroups constructed from quantum Bernoulli noises

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combining the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Leveraging Hamiltonian simulation techniques to compile operations on bosonic devices

Circuit quantum electrodynamics enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e. qubit-oscillator) operations are realizable only through optimal control theory, which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter–Suzuki and Baker–Campbell–Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, namely (a) p (a † ) q for integer p, q. We show examples of this paradigm including obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes–Cummings Hamiltonian, and simulation of the Hong-Ou-Mandel effect. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid qubit-boson devices.

bosonic qubits↗