Microscopic Theory of a System of Interacting Bosons-I : Basic Foundations and Superfluidity

Abstract

Important aspects of a system of interacting bosons like liquid 4 He are critically analyzed to lay down the basic foundations of a new approach to develop its microscopic theory that explains its properties at quantitative level. It is shown that each particle represents a pair of particles (identified as the basic unit of the system) having equal and opposite momenta (q,-q) with respect to their center of mass (CM) that moves as a free particle with momentum K; its quantum state is represented by a macro-orbital which ascribes a particle to have two motions (q and K) of the representative pair. While q is restricted to satisfy q ≥ q o = π/d (d being the nearest neighbor distance) due to hard core inter-particle interaction, K, having no such restriction, can have any value between 0 and ∞. In the ground state of the system, all particles have: (i) q = q o and K = 0, (ii) identically equal nearest neighbor distance r (= d), and (iii) relative phase positions locked at ∆φ (= 2q.r) = 2nπ (n = 1, 2, 3...); they define a close packed arrangement of their wave packets (CPA-WP) having identically equal size, λ/2 = d. The transition to superfluid state represents simultaneous onset of Bose Einstein condensation of particles in the state of q = q o and K = 0 and an order-disorder process which moves particles from their disordered positions in phase space (with ∆φ ≥ 2π in the high temperature phase) to an ordered positions defined by ∆φ = 2nπ (in the low temperature phase). Quantum correlation potentials play an important role in this process. Particles in the superfluid state cease to have relative motion. They develop a kind of collective binding energy (E g (T)), identified as an energy gap between normal liquid state and superfluid state. These inferences help in understanding all significant properties of the superfluid state including loss of viscosity, quantized vortices, critical velocities, infinitely high thermal conductivity, thermo-mechanical and mechano-caloric effects, etc. at quantitative scale; however, this fact is demonstrated in detail, elsewhere.