Quantum Many-Body Theory

<p>This thesis is a collection of theoretical investigations into different aspects of the broad subject of quantum many-body theory. The results are grouped into three main parts, which in turn are divided into separate self-contained sections. Some of the work is presented in the form of published papers and papers that have been submitted for publication. The first section of Part A introduces some of the concepts involved in many-body problems, by developing methods to evaluate expectation values of the form . In the rest of Part A I consider collective excitations of finite quantum systems. The calculations are confined to nuclei because the results can then be compared with the extensive investigations that have been made into collective nuclear modes. In Section AII, wavefunctions are proposed for rotational excitations of even-even nuclei. Both isoscalar and isovector nuclear modes are discussed. In particular, the l2,m> isoscalar states are investigated for both spherical and deformed even-even nuclei, and the simplest isovector wavefunction is shown to give a good description of the giant dipole resonance. In section AIII wavefunctions are proposed for compressional vibrational states of spherical nuclei. Section AIV discusses sum rules for nuclear transitions of a given electric multipolarity. It is found that the 2+ and 1- states investigated in section AII and all but one of the vibrational states discussed in AIII each exhaust a large part of the appropriate sum rule. In Part B I consider the problem of how to describe flow in quantum fluids. In particular, we want to be able to identify the physical motion represented by any given many-body wavefunction. Section BI derives a guantum mechanical velocity field for a many-body system, paying special attention to the need for a quantum continuity equation. It is found that when the wavefunction has the usual time dependence e-iwt , that the quantum velocity formula averages over all oscillatory motion, so that much of the physical nature of the flow field is lost. In section BII a particular wavefunction is proposed to represent the quantum excitation corresponding to any given potential flow field. The results obtained by considering specific examples are very encouraging. In Part C I investigate the properties of surfaces. Section CI presents a theoretical description of the tension, energy and thickness of a classical liquid-vapour interface. In section CII the classical results are extended to describe the surface of a quantum system, namely superfluid helium four. Problems occur for the quantum system if the correlations arising from the zero-point-motion of the phonon modes are included in the ground state wavefunction. Finally, in section CIII discuss generalized virial theorems that give the change in the free energy of a system undergoing an infinitesimal deformation. For example, a particular deformation gives the expression used in CII, for the surface tension of a plane quantum surface.</p>

Quantum Many-Body Theory

<p>This thesis is a collection of theoretical investigations into different aspects of the broad subject of quantum many-body theory. The results are grouped into three main parts, which in turn are divided into separate self-contained sections. Some of the work is presented in the form of published papers and papers that have been submitted for publication. The first section of Part A introduces some of the concepts involved in many-body problems, by developing methods to evaluate expectation values of the form . In the rest of Part A I consider collective excitations of finite quantum systems. The calculations are confined to nuclei because the results can then be compared with the extensive investigations that have been made into collective nuclear modes. In Section AII, wavefunctions are proposed for rotational excitations of even-even nuclei. Both isoscalar and isovector nuclear modes are discussed. In particular, the l2,m> isoscalar states are investigated for both spherical and deformed even-even nuclei, and the simplest isovector wavefunction is shown to give a good description of the giant dipole resonance. In section AIII wavefunctions are proposed for compressional vibrational states of spherical nuclei. Section AIV discusses sum rules for nuclear transitions of a given electric multipolarity. It is found that the 2+ and 1- states investigated in section AII and all but one of the vibrational states discussed in AIII each exhaust a large part of the appropriate sum rule. In Part B I consider the problem of how to describe flow in quantum fluids. In particular, we want to be able to identify the physical motion represented by any given many-body wavefunction. Section BI derives a guantum mechanical velocity field for a many-body system, paying special attention to the need for a quantum continuity equation. It is found that when the wavefunction has the usual time dependence e-iwt , that the quantum velocity formula averages over all oscillatory motion, so that much of the physical nature of the flow field is lost. In section BII a particular wavefunction is proposed to represent the quantum excitation corresponding to any given potential flow field. The results obtained by considering specific examples are very encouraging. In Part C I investigate the properties of surfaces. Section CI presents a theoretical description of the tension, energy and thickness of a classical liquid-vapour interface. In section CII the classical results are extended to describe the surface of a quantum system, namely superfluid helium four. Problems occur for the quantum system if the correlations arising from the zero-point-motion of the phonon modes are included in the ground state wavefunction. Finally, in section CIII discuss generalized virial theorems that give the change in the free energy of a system undergoing an infinitesimal deformation. For example, a particular deformation gives the expression used in CII, for the surface tension of a plane quantum surface.</p>

LITERARY REVIEW ON AGEING PROCESS AND IT'S NATURAL AYURVEDA APPROACH

In Ayurveda, Ageing is termed as ‘Jara’ for which some rules are given to make it healthy with longevity. This is the phase anticipatory care should be taken so that ageing process can be deferred and old age related diseases can be barred. Jara as natural prodigy of human body takes place in two ways i.e. Kalaja and Akalaja. Body gets affected from various factors like diet pattern, food particles, lifestyle, environment, etc. changes or degenerative changes are the nature of universe. These changes are known as Swabhaav in Ayurveda in which a constant decline may found in Shareera in old age. Ageing starts in different attributes at different period; thus, the ancient classics give a detailed version on the physiological, psychological and biological aspects of ageing including growth, puberty and senility.There are enough matter in relation to the establishment and termination of life which can be understood as theory as Theory of Innate Destruction (Swabhawoparamavada), Theory of Disturbance in Fundamental Principle of Body, Theory related to Kala (Time Factor), Theory Related to Environmental and other Biological Aspect. Jara management can be done via programming of lifestyle in such a way that Akalaj Jara can be avoided and Kalaj Jara can be delayed. For this purpose not only the Rasayana drugs but Ayurvediya Dinacharya, Ritucharya and other regimens in the way of ideal lifestyle is to be followed.

Phoretic self-propulsion of helical active particles

Chemically active colloids self-propel by catalysing the decomposition of molecular ‘fuel’ available in the surrounding solution. If the various molecular species involved in the reaction have distinct interactions with the colloid surface, and if the colloid has some intrinsic asymmetry in its surface chemistry or geometry, there will be phoretic flows in an interfacial layer surrounding the particle, leading to directed motion. Most studies of chemically active colloids have focused on spherical, axisymmetric ‘Janus’ particles, which (in the bulk, and in absence of fluctuations) simply move in a straight line. For particles with a complex (non-spherical and non-axisymmetric) geometry, the dynamics can be much richer. Here, we consider chemically active helices. Via numerical calculations and slender body theory, we study how the translational and rotational velocities of the particle depend on geometry and the distribution of catalytic activity over the particle surface. We confirm the recent finding of Katsamba et al. (J. Fluid Mech., vol. 898, 2020, p. A24) that both tangential and circumferential concentration gradients contribute to the particle velocity. The relative importance of these contributions has a strong impact on the motion of the particle. We show that, by a judicious choice of the particle design parameters, one can suppress components of angular velocity that are perpendicular to the screw axis, or even select for purely ‘sideways’ translation of the helix.

Regularized Stokeslets Lines Suitable for Slender Bodies in Viscous Flow

Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent flow. These singularities can be difficult to implement numerically because they diverge at their origin. Hence, people have regularized these singularities to overcome this issue. This regularization blurs the force over a small blob and thereby removing divergent behaviour. However, it is unclear how best to regularize the singularities to minimize errors. In this paper, we investigate if a line of regularized Stokeslets can describe the flow around a slender body. This is achieved by comparing the asymptotic behaviour of the flow from the line of regularized Stokeslets with the results from slender-body theory. We find that the flow far from the body can be captured if the regularization parameter is proportional to the radius of the slender body. This is consistent with what is assumed in numerical simulations and provides a choice for the proportionality constant. However, more stringent requirements must be placed on the regularization blob to capture the near field flow outside a slender body. This inability to replicate the local behaviour indicates that many regularizations cannot satisfy the no-slip boundary conditions on the body’s surface to leading order, with one of the most commonly used blobs showing an angular dependency of velocity along any cross section. This problem can be overcome with compactly supported blobs, and we construct one such example blob, which can be effectively used to simulate the flow around a slender body.

Microscopic Model to Take into Account Complex Configurations for Pygmy and Giant Resonances

A microscopic model for taking into account quasiparticle–phonon interaction in magic nuclei is considered within nuclear quantum many-body theory. This model is of interest for constructing a microscopic theory of pygmy and giant multipole resonances—first of all, a description of their fine structure. This article reports on a continuation and development of our earlier study [1]. Basic physics results of that study are confirmed here, and new results are obtained: (i) exact (not approximate, as in [1]) expressions for the first and second variations of the vertex in the phonon field are found and employed; (ii) a new equation involving, in addition to the known effective interaction, the total amplitude for particle–hole interaction is derived for the vertex, which is the main ingredient in the theory of finite Fermi systems; (iii) the required two-phonon configurations are obtained owing to the last result. The new equation for the vertex now contains complex configurations such as $$1p1h\otimes\textrm{phonon}$$ and two-phonon ones, along with numerous ground-state correlations.

Reaction force of gravitational radiation in an effective-one-body theory based on the post-Minkowskian approximation

Effective-one-body (EOB) theory based on the post-Newtonian (PN) approximation presented by Buonanno and Damour plays an important role in the analysis of gravitational wave signals. Based on the post-Minkowskian (PM) approximation, Damour introduced another novel EOB theory which will lead to theoretically improved versions of the EOB conservative dynamics and might be useful in the upcoming era of high signal-to-noise-ratio gravitational-wave observations. Using the 2PM effective metric obtained by us recently, in this paper we study the radiation reaction force experienced by the particle with the help of the energy-loss-rate, which is an important step to construct the EOB theory based on the PM approximation.