Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction

**degrees**

**of**

**freedom**modeling a chemical reaction, yet it exhibits behaviour that is still not well understood - the reaction rate decreases as a function

**of**energy beyond a critical value. Using lobe dynamics we show how invariant manifolds

**of**unstable periodic orbits guide trajectories in phase space. From the structure

**of**the invariant manifolds we deduce that insufficient transfer

**of**energy between the

**degrees**

**of**

**freedom**causes a reaction rate decrease. In physical terms this corresponds to the free hydrogen atom repelling the whole molecule instead

**of**only one atom from the molecule. We further derive upper and lower bounds

**of**the reaction rate, which are desirable for practical reasons.

4/10 relevant

arXiv

On the **Degrees** **of** **Freedom** of the MISO Interference Broadcast Channel
with Delayed CSIT

**degrees**

**of**

**freedom**(DoF) that can be achieved for the broadcast channel (BC). Since its appearance, many works have extended the concept

**of**Retrospective Interference Alignment (RIA) to other multi-user channel configurations. However, little is known about the broadcast channel with multiple cells, i.e. the interference broadcast channel (IBC). In this work, the DoF are studied for the $K$-user $C$-cell multiple-input single-output (MISO) IBC with delayed CSIT (with $K/C$ users per cell). We show that the straightforward application

**of**the MAT scheme over the IBC fails because it requires all interference to be received from the same source. Hence, in this case not all the interference can be cancelled, thus blocking the decoding

**of**the received messages. We call this phenomenon as \textit{interference coupling}, forcing to use the MAT scheme by serving just one cell at a time. In this work, we propose an extension, namely the uncoupled MAT scheme (uMAT), exploiting multiple cells, uncoupling the interference, and achieving the best known DoF inner bound for almost all settings.

10/10 relevant

arXiv

BeamDelta: simple alignment tool for optical systems

**of**the current laser beam position and a reference position. Even a simple optical setup has multiple

**degrees**

**of**

**freedom**that affect the alignment

**of**beam paths. These

**degrees**

**of**

**freedom**rise exponentially with the complexity

**of**the system. The process

**of**aligning all the optical components for a specific system is often esoteric and poorly documented, if it is documented at all. Alignment methods used often rely on visual inspection

**of**beams impinging on pinholes in the beam path. Typically requiring an experienced operator staring at diffuse reflections for extended periods

**of**time. This can lead to a decline in accuracy due to eye strain, flash blindness as well as symptoms such as headaches and, possibly, more serious retinal damage. Here we present BeamDelta a simple alignment tool and accompanying software interface which allows users to obtain accurate alignment as well as removing the necessity

**of**staring at diffuse laser reflections. BeamDelta is a robust alignment tool as it doesn't require any precise alignment itself.

5/10 relevant

bioRxiv

Probing the partonic **degrees** **of** **freedom** in high multiplicity p-Pb
collisions at $\sqrt{s_{NN}}=$ 5.02 TeV

**of**partonic

**degrees**

**of**

**freedom**in high multiplicity p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV, based on the coalescence model for the production

**of**intermediate transverse momentum $p_T$ using soft partons from the VISH2+1 hydrodynamics and hard partons from the LBT energy loss model. This coalescence model is further smoothly connected with the hydrodynamic model for the production

**of**low $p_T$ hadrons and the jet fragmentation for the production

**of**high $p_T$ hadrons to provide a nice description

**of**the $p_T$-spectra

**of**pions, kaons and protons as well as their differential elliptic flows over the $p_T$ range from 0 to 6 GeV. We further show that quark coalescence contributions lead to an approximate number

**of**constituent quark scaling

**of**elliptic flows at intermediate $p_T$ as observed in experiments. Our result demonstrates the importance

**of**the partonic

**degrees**

**of**

**freedom**and the possible formation

**of**QGP in high multiplicity p+Pb collisions at the LHC.

10/10 relevant

arXiv

Competition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath

**of**the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range

**of**systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath

**of**non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending on whether the Kitaev couplings are greater or less than the Kondo temperature. We characterize the ground state properties

**of**the system and determine the temperature dependence

**of**the crossover scale for the emergence

**of**fractionalized

**degrees**

**of**

**freedom**in the model. We also demonstrate qualitatively as well as quantitatively that in the Kondo limit, the complex impurity can be mapped to an effective two-impurity system, where the emergent spin $1/2$ comprises

**of**both Majorana and flux

**degrees**

**of**

**freedom**. For a tetrahedral-shaped Kitaev cluster, an extra orbital

**degree**

**of**

**freedom**closely related to a flux

**degree**

**of**

**freedom**remains unscreened even in the presence

**of**both Heisenberg and Kondo interactions.

4/10 relevant

arXiv

Unsupervised decoding **of** spinal motor neuron spike trains for estimating
hand kinematics following targeted muscle reinnervation

**degrees**

**of**

**freedom**. Expand abstract.

**of**upper-limb prostheses is currently limited by the relatively poor functionality

**of**unintuitive control schemes. This paper proposes to extract, from multichannel electromyographic signals (EMG), motor neuron spike trains and project them into lower dimensional continuous signals, which are used as multichannel proportional inputs to control the prosthetic's actuators. These control signals are an estimation

**of**the common synaptic input that the motor neurons receive. We use the simplest

**of**metric learning approaches known as principal component analysis (PCA), as a linear unsupervised metric projection to extract the spectral information

**of**high dimensional data into the subspace

**of**the prosthetic hand

**degrees**

**of**

**freedom**. We also investigate the importance

**of**a rotation in the projection space that best aligns the PCA subspace with the space

**of**

**degrees**

**of**

**freedom**

**of**the prosthetic hand, to attempt to approximate the sparseness properties

**of**the motor axes (which are orthogonal), while no sparseness is enforced by PCA. Proof

**of**concept for the feedforward path (open loop) is given by successful estimation

**of**concurrent movements with up to three

**degrees**

**of**

**freedom**. We also analyze and quantify the performance

**of**the proposed decoding algorithm under implementation constraints and hardware limitations and propose a space-time subsampling strategy, to maximize projection fidelity, in each extracted source over time. The results confirm that the proposed decoding approach can directly project the motor neuron spike trains into kinematics for simultaneous and proportional prosthesis control that can be extended to multiple

**degrees**

**of**

**freedom**. We show that the method is robust to reducing the training data in space (number

**of**sources) and time, which makes it potentially suitable for clinical applications.

7/10 relevant

arXiv

Non-reciprocal hidden **degrees** **of** **freedom**: A unifying perspective on
memory, feedback, and activity

**degrees**

**of**

**freedom**renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. Expand abstract.

**of**these intrinsically nonequilibrium systems are reproduced by low-dimensional Markovian networks with NR coupling, which we establish as minimal models for such complex systems. NR coupling alone implies a violation

**of**the fluctuation-dissipation relation, which is inevitably connected to entropy production, i.e., irreversibility. Hiding the NR coupled

**degrees**

**of**

**freedom**renders non-Markovian, one-variable Langevin descriptions with complex types

**of**memory, for which we find a generalized second law involving information flow. We demonstrate that non-monotonic memory is inextricably linked to NR coupling. Furthermore, we discuss discrete time delay as the infinite-dimensional limit, and find a divergent entropy production, corresponding to unbounded cost for precisely storing a Brownian trajectory.

8/10 relevant

arXiv

Certification **of** high-dimensional entanglement generated in
Hong-Ou-Mandel interference

**degrees**

**of**

**freedom**, in particular in the context of high-dimensional quantum information processing protocols. Expand abstract.

**of**quantum information processing tasks. Harnessing the generation and characterization

**of**entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency

**degrees**

**of**

**freedom**(DOF). We show how independent measurements

**of**polarization and frequency DOF allow for both the verification and, strictly stronger requirement, also the certification

**of**high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation

**of**entanglement stored in multiple

**degrees**

**of**freedom, in particular in the context

**of**high-dimensional quantum information processing protocols.

5/10 relevant

arXiv

Emergent ballistic transport **of** Bose-Fermi mixtures in one dimension

**of**two decoupled Luttinger liquids with bosonic and fermionic

**degrees**

**of**

**freedom**at low temperatures. However, the transport properties

**of**such decoupled Luttinger liquids

**of**charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties

**of**one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves

**of**two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction point $x=0$. Using the Bethe ansatz solution, we first rigorously prove the existence

**of**conserved charges for both the bosonic and fermionic

**degrees**

**of**freedom, preserving the Euler-type continuity equations. We then analytically obtain the distributions

**of**the densities and currents

**of**the local conserved quantities which solely depend on the ratio $\xi=x/t$. The left and right moving quasiparticle excitations

**of**the two halves form multiple segmented light-cone hydrodynamics that display ballistic transport

**of**the conserved charge densities and currents in different

**degrees**

**of**

**freedom**. Our analytical results provide a deep understanding

**of**the quantum transport

**of**multi-component Luttinger liquids in quantum systems with both bosonic and fermionic statistics.

7/10 relevant

arXiv

The quasilocal **degrees** **of** **freedom** of Yang-Mills theory

**of**boundaries, inevitably lead to subtleties. In the $D+1$ formulation

**of**Yang-Mills theories, we employ a generalized Helmholtz decomposition to (i) identify the quasilocal radiative and pure-gauge/Coulombic components

**of**the gauge and electric fields, and to (ii) study the properties

**of**these components upon gluing

**of**regions. Being rooted in the geometry

**of**the Yang-Mills configuration space, our decomposition is naturally carried to the symplectic structure

**of**the theory, similarly decomposing it into a (bulk) radiative and a (pure-boundary) Coulombic part. Whereas the former encodes the intrinsic physical content

**of**a region, the latter displays interesting features that e.g. justify the superselection

**of**the electric flux through the boundary. Concerning the gluing

**of**a topologically-trivial bipartite system, we prove a formula that uniquely reconstructs the global radiative components

**of**the fields from their regional counterparts. In the same setup, we also prove that knowledge

**of**both regional radiative components

**of**the electric field also suffices to reconstruct its regional Coulombic components: they are found to be functionals

**of**the mismatch

**of**the regional radiatives at the interface between the two regions. But gluing is not always unique: for non-simply connected manifolds or for reducible field configurations, identical regional radiative modes may be glued into physically distinct global configurations. At reducible configurations, the ambiguity is related to the existence

**of**nontrivial color charges, while the topological ambiguity is are due to the presence

**of**global Aharonov-Bohm modes. In an appendix, we revisit Dirac's dressing

**of**charged particles in the non-Abelian context, thus providing an independent entry point to the geometrical tools subsuming our generalized Helmholtz decomposition.

8/10 relevant

arXiv