Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Modern quantum theory.

Includes bibliography.

Quantum theory of scattering

Includes bibliography.

The quantum theory.

Mode of access: Internet.

Quantum theory, with applications to chemistry.

Reproduced from typewritten copy.

On the quantum theory of line-spectra,

Issued in three parts.

Synapses, quantum theory and panpsychism

The introduction situates the ‘hard problem’ in its historical context and argues that the problem has two sides: the output side (the Kant-Eccles problem of the freedom of the Will) and the input side (the problem of qualia). The output side ultimately reduces to whether quantum mechanics can affect the operation of synapses. A discussion of the detailed molecular biology of synaptic transmission as presently understood suggests that such affects are unlikely. Instead an evolutionary argument is presented which suggests that our conviction of free agency is an evolutionarily induced illusion and hence that the Kant-Eccles problem is itself illusory. This conclusion is supported by well-known neurophysiology. The input side, the problem of qualia, of subjectivity, is not so easily outflanked. After a brief review of the neurophysiological correlates of consciousness (NCC) and of the Penrose-Hameroff microtubular neuroquantology it is again concluded that the molecular neurobiology makes quantum wave-mechanics an unlikely explanation. Instead recourse is made to an evolutionarily- and neurobiologically-informed panpsychism. The notion of an ‘emergent’ property is carefully distinguished from that of the more usual ‘system’ property used by most dual-aspect theorists (and the majority of neuroscientists) and used to support Llinas’ concept of an ‘oneiric’ consciousness continuously modified by sensory input. I conclude that a panpsychist theory, such as this, coupled with the non-classical understanding of matter flowing from quantum physics (both epistemological and scientific) may be the default and only solution to the problem posed by the presence of mind in a world of things.

Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Black hole scattering from Worldline Quantum Field Theory and the Classical Double Copy of Spinning particles

This PhD thesis focuses on studying the classical scattering of massive/massless particles toward black holes, and investigating double copy relations between classical observables in gauge theories and gravity. This is done in the Post-Minkowskian approximation i.e. a perturbative expansion of observables controlled by the gravitational coupling constant κ = 32πGN, with GN being the Newtonian coupling constant. The investigation is performed by using the Worldline Quantum Field Theory (WQFT), displaying a worldline path integral describing the scattering objects and a QFT path integral in the Born approximation, describing the intermediate bosons exchanged in the scattering event by the massive/massless particles. We introduce the WQFT, by deriving a relation between the Kosower- Maybee-O’Connell (KMOC) limit of amplitudes and worldline path integrals, then, we use that to study the classical Compton amplitude and higher point amplitudes. We also present a nice application of our formulation to the case of Hard Thermal Loops (HTL), by explicitly evaluating hard thermal currents in gauge theory and gravity. Next we move to the investigation of the classical double copy (CDC), which is a powerful tool to generate integrands for classical observables related to the binary inspiralling problem in General Relativity. In order to use a Bern-Carrasco-Johansson (BCJ) like prescription, straight at the classical level, one has to identify a double copy (DC) kernel, encoding the locality structure of the classical amplitude. Such kernel is evaluated by using a theory where scalar particles interacts through bi-adjoint scalars. We show here how to push forward the classical double copy so to account for spinning particles, in the framework of the WQFT. Here the quantization procedure on the worldline allows us to fully reconstruct the quantum theory on the gravitational side. Next we investigate how to describe the scattering of massless particles off black holes in the WQFT.

Quantum information and quantum communication theory in relation to black hole idealized mechanical models

Oggigiorno il concetto di informazione è diventato cruciale in fisica, pertanto, siccome la migliore teoria che abbiamo per compiere predizioni riguardo l'universo è la meccanica quantistica, assume una particolare importanza lo sviluppo di una versione quantistica della teoria dell'informazione. Questa centralità è confermata dal fatto che i buchi neri hanno entropia. Per questo motivo, in questo lavoro sono presentati elementi di teoria dell'informazione quantistica e della comunicazione quantistica e alcuni sono illustrati riferendosi a modelli quantistici altamente idealizzati della meccanica di buco nero. In particolare, nel primo capitolo sono forniti tutti gli strumenti quanto-meccanici per la teoria dell'informazione e della comunicazione quantistica. Successivamente, viene affrontata la teoria dell'informazione quantistica e viene trovato il limite di Bekenstein alla quantità di informazione chiudibile entro una qualunque regione spaziale. Tale questione viene trattata utilizzando un modello quantistico idealizzato della meccanica di buco nero supportato dalla termodinamica. Nell'ultimo capitolo, viene esaminato il problema di trovare un tasso raggiungibile per la comunicazione quantistica facendo nuovamente uso di un modello quantistico idealizzato di un buco nero, al fine di illustrare elementi della teoria. Infine, un breve sommario della fisica dei buchi neri è fornito in appendice.

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing the interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to the previously established classical limit with a classical field behavior, showing that the limit h -> 0 of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Measurement and state preparation via ion trap quantum computing

We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'HELON and G. J. MILBURN, Phys Rev. A 54, 5141 (1996)]. The performance of a measurement shows some interesting patterns which are closely related to searching.

Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.