The Four-Dimensional XY Spin Glass

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite- size scaling analysis of the data leads to a finite temperature spin glass transition at $T_c=0.95\pm 0.15$. The critical exponents are estimated to be $\nu_{sg}=0.70\pm 0.10$ and \eta_{sg}=-0.28\pm 0.38$. The results imply that the lower critical dimensionality for the XY spin glass is less than four.Comment: 13 pages, TeX; 4 figures available on request from [email protected]

Untouched aspects of the wave mechanics of a particle in one dimensional box

Wave mechanics of a particle in 1-D box (size $= d$) is critically analyzed to reveal its untouched aspects. When the particle rests in its ground state, its zero-point force ($F_o$) produces non-zero strain by modifying the box size from $d$ to $d' = d + \Delta d$ in all practical situations where the force ($F_a$) restoring $d$ is not infinitely strong. Assuming that $F_a$ originates from a potential $\propto x^2$ ($x$ being a small change in $d$), we find that: (i) the particle and strained box assume a mutually bound state (under the equilibrium between $F_o$ and $F_a$) with binding energy $\Delta{E} = -\epsilon_o'\Delta{d}/d'$ (with $\epsilon_o' = h^2/8md'^2$ being the ground state energy of the particle in the strained box), (ii) the box size oscillates around $d'$ when the said equilibrium is disturbed, (iii) an exchange of energy between the particle and the strained box occurs during such oscillations, and (iv) the particle, having collisional motion in its excited states, assumes collisionless motion in its ground state. These aspects have desired experimental support and proven relevance for understanding the physics of widely different systems such as quantum dots, quantum wires, trapped single particle/ion, clusters of particles, superconductors, superfluids, {\it etc.} It is emphasized that the physics of such a system in its low energy states can be truly revealed if the theory incorporates $F_o$ and related aspects.Comment: 8 pages no figur

The p=0 condensate is a myth

Analyzing some of the basic aspects of the dynamics of two bosons (interacting through a central force) and their importance in determining the ground state of a system like liquid $^4He$, it is unequivocally concluded that our conventional belief in the existence $p=0$ condensate in the superfluid state of such systems [including the state of Bose Einstein condensate (BEC) of trapped dilute gases] is a myth.Comment: 9 pages including 1 figur

Ground State of a System of N Hard Core Quantum Particles in 1D Box

The ground state of a system of $N$ impenetrable hard core quantum particles in a 1-D box is analyzed by using a new scheme applied recently to study a similar system of two such particles {\it [Centl. Eur. J. Phys., 2(4), 709 (2004)]}. Accordingly, each particle of the system behaves like an independent entity represented by a {\it macro-orbital}, -a kind of pair waveform identical to that of a pair of particles moving with ($q$, $-q$) momenta at their {\it center of mass} which may have any momentum $K$ in the laboratory frame. It concludes: (i) $= 0$, (ii) $\ge \lambda/2$ and (iii) $q \ge q_o (= \pi/d)$ (with $d = L/N$ being the average nearest neighbour distance), {\it etc.} While all bosons in their ground state have $q = q_o$ and $K = 0$, fermions have $q= q_o$ with different $K$ ranging between 0 and $K = K_F$ (the Fermi wave vector). Independent of their bosonic or fermionic nature, all particles in the ground state define a close packed arrangement of their equal size wave packets representing an ordered state in phase ($\phi-$)space with $\Delta\phi = 2n\pi$ (with $n$ = 1,2,3, ...), $= \lambda/2 = d$, and $q = q_o$. As such our approach uses greatly simplified mathematical formulation and renders a visibly clear picture of the low energy states of the systems and its results supplement earlier studies in providing their complete understanding.Comment: 19 pages, no figure

Experimental realities refuting the existence of p=0 condensate in a system of interacting bosons : II. Spectroscopy of embedded molecules

Experimental observation of superfluidity in a microscopic cluster, $M:(^4He)_x$, of a molecule ($M$) and $x$ number of $^4He$ atoms (with $x$ ranging from 1 to many) is qualitatively analyzed. It concludes that: (i) each $^4He$ atom in the cluster has to have non-zero momentum for its confinement to a space of size ($<$ the size of the cluster), (ii) superfluidity does not require atoms with zero momentum ($p=0$), and (iii) while all $^4He$ atoms in the cluster cease to have relative motions (hence the inter-atomic collisions), they retain a freedom to move coherently in order of their locations on a closed path around the rotor ($M$ plus few nearest $^4He$ atoms which follow the molecular rotation for their relatively strong binding with $M$). The analysis also identifies the basic arrangement of $^4He$ atoms which allows the rotor to have free rotation in the cluster.Comment: 6 pages, 1 figur

Unified Microscopic Theory of a System of Interacting Bosons

This paper reports the unified microscopic theory of a system of interacting bosons such as liquid $^4He$.Each particle in the system represents a $(q;-q)$ pair moving with a centre of mass momentum K.Particles form bound pairs below $\lambda$-point and have a kind of collection binding between them.The binding is idenified as an energy gap between the superfluid and the normal states of the system.The $\lambda$-transition is a consequence of interparticle quantum correlations.It follows an order-disoder of particles in their phase structure as well as the onset of Bose_ Einstein condensatin in the state of $q={\pi}/d$ and K=0.In addition to the well known modes of collective motion such as photons,rotons, maxons etc.,the superfluid state also exhibits a new kind of quasi-particle,omon,characterised by a phononlike wave of the oscillations of the momentum coordinates of the particle.The theory explains the properties of $He-II$ at quantitative level and vindicates the two-fluid theory of Landau.The paper finally describes the way this theory could help in understanding the superfluidity of 1-D and 2-D systems.It also analyses the possibility of applying this approach to develop similar framework for a fermion system including an atomic nucleus.Comment: 20 pages,LATE

Experimental realities refuting existence of p=0 condensate in a system of interacting bosons : I. Electron bubble

Physical reality of the existence of electron bubble in liquid $^4He$ (or $^3He$) renders a {\it clear experimental evidence} for a quantum particle (in an interacting environment as seen by electron in liquid helium) to occupy exclusively a space of size $\lambda/2$ that, obviously, depends on its energy/momentum. This unequivocally proves that {\it no particle} in a system of interacting bosons such as liquid $^4He$ has momentum $p=0$; in stead, {\it all particles} in the ground state of such a system are in the single quantum state of energy $\varepsilon_o = h^2/8md^2$ or momentum $p = h/2d$.Comment: 6 pages 1 figur

Basic Problems of a Microscopic Theory of a Many Body Quantum System

Basic problems of a microscopic theory of many body quantum systems and different aspects of a new approach which can help in solving them are discussed in detail. To this effect we make a critical study of the wave mechanics of two hard core quantum particles and discover its several untouched aspects, viz.: (i) the useful details of \psi_k(r) (representing the relative motion of two particles), (ii) the expectation value of hard core (HC) repulsion (), (iii) the inconsistency of the statements, r \le\sigma and \psi_k(r \le\sigma)=0 (\sigma=HC diameter of a particle), with uncertainty principle particularly for low k values, (iv) the lower bound of allowed values of k=2q, (v) the dominance of interparticle phase correlation in low temperature phase. For the first time this study concludes that has zero value which does not agree with its non-zero value known for the last several decades. This also finds compelling reasons for a system of interacting bosons such as liquid ^4He to have (q, -q) pair condensation with allowed q, obviously controlled by V_{HC}(r), to satisfy q \ge\pi/d. Several important aspects of N body quantum systems like liquids ^4He and ^3He are also concluded. Free from any error [see editor's note J. Scientific Exploration 16(1), p.1 (2002)], our approach can help in developing nearly exact microscopic theories of widely different systems of interacting bosons and fermions, as demonstrated for liquids ^4He type systems [J. Scientific Exploration, 16, 77-116 (2002)]. The paper also sums up the expert observations with our response to facilitate one to have a critical assessment and better understanding of the new approach.Comment: 9 pages, RevTeX, No figure

A Study of Elementary Excitations of Liquid Helium-4 Using Macro-orbital Microscopic Theory

Energy of elementary excitations and the anomalous nature of small Q phonons in He-II are studied by using our macro-orbital microscopic theory of a system of interacting bosons (cond-mat/0606571). It is observed that : (i) the experimental E(Q) of He-II not only agrees with our theoretical relation $E(Q) = \hbar^2Q^2/4mS(Q)$ but also supports an important conclusion of Price that S(0) should have zero value for quantum fluids, and (ii) Feynman's energy of excitations $E(Q)_{Fyn} = \hbar^2Q^2/2mS(Q)$ equals approximately to $2E(Q)_{exp}$ even at low Q. Three problems with the Feynman's inference that $E(Q)_{Fyn}$ has good agreement with $E(Q)_{exp}$ at low Q are identified. It is argued that the theory can also be used to understand similar spectrum of the BEC state of a dilute gas reported by O'Dell et al.Comment: 13 pages with 4 figure

Persistence in Random Bond Ising Models of a Socio-Econo Dynamics in High Dimensions

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to 5. The model includes a ` social\rq local field which contains the magnetization at time $t$. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, $p$. The decay of the persistence probability in the model depends on both the spatial dimension and $p$. We find no evidence of ` blocking\rq in this model. We also discuss the implications of our results for applications in the social and economic fields.Comment: 9 pages, 4 figure