Harris criterion In studies of the phase-transition phenomena, the systems considered before were assumed to be perfectly homogeneous. In real physical systems, however, some defects or impurities are always present. Therefore, it is natural to consider what effect impurities might have on the phase-transition phenomena. As we have seen in the previous chapter, the thermodynamics of the second-order phase transition is dominated by large-scale fluctuations. The dominant scale, or the correlation length, R c ∼ | T / T C – l| – v grows as T approaches the critical temperature T c , where it becomes infinite. The large-scale fluctuations lead to singularities in the thermodynamical functions as |τ| ≡ | T / T c – 1| → 0. These singularities are the main subject of the theory. If the concentration of impurities is small, their effect on the critical behavior remains negligible so long as R c is not too large, i.e. for T not too close to T c . In this regime the critical behavior will be essentially the same as in the perfect system. However, as |τ| → 0 ( T → T c ) and R c becomes larger than the average distance between impurities, their influence can become crucial. As T c is approached the following change of length scale takes place. First, the correlation length of the fluctuations becomes much larger than the lattice spacing, and the system ‘forgets’ about the lattice. The only relevant scale that remains in the system in this regime is the correlation length R c (τ).
Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.
A richly diverse range of phenomena and applications, frequently in the context of laser applications, owe their means of operation to the properties of the photon. Yet, since the arrival of the laser, the distinctive and often paradoxical nature of the photon has become more than ever evident, and what the optics community now understands by a ‘photon’ has become richer – certainly less simple, than Einstein’s original conception. There has been a marked expansion in the pace of development since the now familiar derivative term ‘photonics’ first emerged, and in much current theory any dividing line between ‘real’ and ‘virtual’ photons proves to be illusory. So if, in this technical sense, no photon can ever be regarded as entirely real, one is drawn to deeper questions of whether the photon is ‘real’ in the broader sense of reality. Some would argue that electromagnetic fields are closer to irreducible reality. Yet whether we elect to describe optical phenomena in terms of fields or photons, neither represents what is actually measured. The surest ground has to be found where theory is cast in terms that explain or predict actual observations, under given conditions. It is consistent with the path integral formulation of quantum mechanics that derivations should not prescribe what intervenes between setup and measurement, but instead allow for all possibilities. Indeed, one of the beauties of the associated mathematics is its capacity to home in on possibilities that most closely conform to post-event physical interpretation. Still, we can ask: how much do or can we know about the photon itself? How much information could this entity contain or convey? And, how essential is a photonic formulation of theory? This study focuses on some of the key issues.
Abstract As space missions—both manned and unmanned—expand beyond Earth’s orbit, the need for reliable and real-time communication between Earth and distant spacecraft becomes critical. Conventional radio-frequency communication is constrained by the speed of light, resulting in significant signal delays; for example, a message to Mars experiences a minimum one-way delay of approximately 8 minutes. Such delays hinder operational control and decision-making during critical maneuvers or emergencies. This paper explores quantum communication as a potential solution, leveraging quantum entanglement and superposition to establish instantaneous correlations between remote systems. By employing these quantum phenomena, it becomes theoretically possible to achieve real-time information exchange independent of conventional speed-of-light limitations. The study discusses foundational principles, potential implementation in space systems, and implications for future deep-space exploration.