The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
In many-body quantum systems at ultra‑low temperatures, the collective behavior of particles can give rise to exotic states of matter such as superfluids and quantum liquids. These states exhibit macroscopic quantum coherence and support topological excitations, yet their internal mechanical response has traditionally been described only by local thermodynamic variables such as pressure, density, and temperature. In this work we introduce the concept of a topological pressure field, denoted PT(x), which captures the influence of non‑trivial topological order on the local mechanical pressure within a quantum liquid. The proposed field is derived from a gauge‑invariant formulation of the quantum stress tensor that incorporates Berry curvature and Chern‑Simons terms. We show that PT(x) is non‑zero only in regions where the quantum state hosts topological defects such as quantized vortices or skyrmion‑like textures. Using a simplified model of a two‑dimensional superfluid film, we calculate the spatial profile of PT(x) around a vortex core and predict measurable deviations from the classical pressure distribution. The existence of PT(x) implies that quantum liquids possess an additional mechanical degree of freedom that is purely topological. This insight opens a pathway to experimentally detect topological pressure via precision pressure sensors in superfluid helium or cold‑atom Bose‑Einstein condensates, and suggests new avenues for engineering quantum fluid devices that exploit topological mechanics.
The concept of a stress tensor is fundamental in classical continuum mechanics, encapsulating internal forces per unit area that a material can sustain. In quantum many‑body systems, however, the notion of pressure and stress has traditionally been limited to scalar or local quantities derived from the equation of state or from density functional approximations. In this work we introduce a fully tensorial representation of electronic internal forces that arises naturally from the quantum mechanical description of electrons in condensed matter systems. We define the Electron Quantum Stress Tensor (EQST) as a second‑rank tensor operator constructed from the kinetic and interaction contributions to the many‑electron Hamiltonian. By deriving explicit expressions for the EQST in terms of the electron density, its gradients, and the exchange–correlation potential, we establish a direct link between the microscopic wavefunction and macroscopic mechanical observables. The EQST framework provides a new lens for interpreting phenomena in two‑dimensional electron gases, quantum Hall fluids, and other strongly correlated electronic materials, offering a potential route toward uncovering novel mechanical properties of electrons that could have implications for future Nobel‑level discoveries.
In conventional quantum theory, the evolution of a pure state is governed solely by the Hamiltonian operator via the Schrödinger equation, without any explicit dependence on spatial derivatives of the state vector beyond the kinetic term. This paper introduces a novel concept, the Quantum State Pressure Gradient (QSPG), which posits that the Hilbert space of quantum states possesses an intrinsic pressure field that varies with the state's configuration. By defining a pressure scalar P_psi associated with the state |psi>, we derive a pressure gradient nabla P_psi that acts as an additional driving force in the dynamical equations. The modified evolution equation incorporates this gradient term, leading to corrections to the standard quantum dynamics that become significant in regimes of strong spatial inhomogeneity or high state density. We present the mathematical formulation of the QSPG, derive the associated continuity and energy equations, and discuss the physical implications. Potential experimental verification is proposed using quantum simulators capable of engineering tailored potentials and measuring state-dependent pressure-like observables. The QSPG framework offers a fresh perspective on quantum dynamics, with implications ranging from quantum thermodynamics to the foundations of quantum mechanics, and may provide a pathway toward new Nobel‑prize level discoveries.
In conventional fluids, acoustic excitations are described by the propagation of pressure and density fluctuations obeying the linearized Euler equations. In contrast, a superfluid—being a macroscopic quantum state with zero viscosity—supports excitations that are governed by the Gross–Pitaevskii equation and exhibit a linear dispersion at low momenta. Here we propose a novel type of excitation in superfluids, which we term "quantum pressure waves" (QPWs). A QPW is a localized, solitonic modulation of the quantum pressure term that appears in the Madelung formulation of the Gross–Pitaevskii equation. Unlike ordinary sound, a QPW does not carry a classical pressure gradient but instead represents a self‑consistent rearrangement of the quantum potential that propagates without dissipation. We develop an analytic theory of QPWs, derive their dispersion relation, and discuss their stability properties. The existence of QPWs suggests a new class of quantum fluid dynamics and points toward possible experimental observation in ultracold atomic gases.
Ultrafast dynamics of collective excitations in superfluids remains largely unexplored beyond the roton region of the Landau excitation spectrum, despite the importance of such dynamics for understanding nonequilibrium processes in these systems. Here, we employ ultrafast coherent control with sequences of femtosecond pulses to perform spectroscopy of multiple quasiparticles in superfluid helium far from equilibrium. By measuring the time-resolved optical birefringence, we track the nonequilibrium dynamics of quasiparticle pairs associated with rotons, maxons and the Pitaevskii plateau region. The spectral lineshape of the roton peak is explained by an ab initio theoretical analysis of the roton-roton interaction. We also reveal strong energy shifts and short lifetimes of both maxon and Pitaevskii-plateau pairs, as well as an influence of the quasiparticle effective mass on the phase of their coherent response to laser pulses. These results demonstrate the ability to extract previously inaccessible information about collective excitations in a strongly interacting quantum fluid by probing its nonequilibrium dynamics on picosecond and sub-picosecond timescales.